Generate this sequence more efficiently

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4












$begingroup$


Is there a more effecient way to generate the sequence shown below.



createOrder[n_] := 
Which[OddQ[n],
Join[Table[2 i - 1, i, 1, (n + 1)/2],Reverse@Table[2 i, i, 1, (n + 1)/2]],
EvenQ[n],
Join[Table[2 i - 1, i, 1, n/2 + 1],Reverse@Table[2 i, i, 1, n/2]]]


createOrder[#] & /@ Range[8] // MatrixForm


table










share|improve this question











$endgroup$
















    4












    $begingroup$


    Is there a more effecient way to generate the sequence shown below.



    createOrder[n_] := 
    Which[OddQ[n],
    Join[Table[2 i - 1, i, 1, (n + 1)/2],Reverse@Table[2 i, i, 1, (n + 1)/2]],
    EvenQ[n],
    Join[Table[2 i - 1, i, 1, n/2 + 1],Reverse@Table[2 i, i, 1, n/2]]]


    createOrder[#] & /@ Range[8] // MatrixForm


    table










    share|improve this question











    $endgroup$














      4












      4








      4





      $begingroup$


      Is there a more effecient way to generate the sequence shown below.



      createOrder[n_] := 
      Which[OddQ[n],
      Join[Table[2 i - 1, i, 1, (n + 1)/2],Reverse@Table[2 i, i, 1, (n + 1)/2]],
      EvenQ[n],
      Join[Table[2 i - 1, i, 1, n/2 + 1],Reverse@Table[2 i, i, 1, n/2]]]


      createOrder[#] & /@ Range[8] // MatrixForm


      table










      share|improve this question











      $endgroup$




      Is there a more effecient way to generate the sequence shown below.



      createOrder[n_] := 
      Which[OddQ[n],
      Join[Table[2 i - 1, i, 1, (n + 1)/2],Reverse@Table[2 i, i, 1, (n + 1)/2]],
      EvenQ[n],
      Join[Table[2 i - 1, i, 1, n/2 + 1],Reverse@Table[2 i, i, 1, n/2]]]


      createOrder[#] & /@ Range[8] // MatrixForm


      table







      list-manipulation table sequence






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Jan 18 at 10:11









      Henrik Schumacher

      52.4k470147




      52.4k470147










      asked Jan 18 at 7:09









      Hubble07Hubble07

      2,988721




      2,988721




















          3 Answers
          3






          active

          oldest

          votes


















          4












          $begingroup$

          cg = Compile[a, _Integer, 1, b, _Integer, 1, i, _Integer,
          Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
          CompilationTarget -> "WVM",
          RuntimeAttributes -> Listable,
          Parallelization -> True
          ];
          g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





          share|improve this answer











          $endgroup$












          • $begingroup$
            there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
            $endgroup$
            – Jerry
            Jan 18 at 10:01











          • $begingroup$
            Good point, I added the pattern after posting...
            $endgroup$
            – Henrik Schumacher
            Jan 18 at 10:10


















          6












          $begingroup$

          ClearAll[f]
          f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
          TeXForm @ MatrixForm @ f[8]



          $left(
          beginarrayc
          1,2 \
          1,3,2 \
          1,3,4,2 \
          1,3,5,4,2 \
          1,3,5,6,4,2 \
          1,3,5,7,6,4,2 \
          1,3,5,7,8,6,4,2 \
          endarray
          right)$




          Also



          ClearAll[f2, f3]
          f2[n_Integer] := SortBy[Range@#, EvenQ, -# (-1 )^Mod[#, 2] &] & /@ Range[2, n]
          f3[n_] := Ordering[Transpose[-Mod[#, 2], -# (-1 )^Mod[#, 2] &@Range[#]]] & /@ Range[2, n]

          f[8] == f2[8] == f3[8]



          True







          share|improve this answer











          $endgroup$




















            5












            $begingroup$

             fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest

            fGetList[10] // MatrixForm // TeXForm


            $
            left(
            beginarrayc
            1,2 \
            1,3,2 \
            1,3,4,2 \
            1,3,5,4,2 \
            1,3,5,6,4,2 \
            1,3,5,7,6,4,2 \
            1,3,5,7,8,6,4,2 \
            1,3,5,7,9,8,6,4,2 \
            1,3,5,7,9,10,8,6,4,2 \
            endarray
            right)$



            another version



            fGetList2[n_?IntegerQ] := 
            Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]

            fGetList2[10] // MatrixForm // TeXForm


            $left(
            beginarrayc
            1,2 \
            1,3,2 \
            1,3,4,2 \
            1,3,5,4,2 \
            1,3,5,6,4,2 \
            1,3,5,7,6,4,2 \
            1,3,5,7,8,6,4,2 \
            1,3,5,7,9,8,6,4,2 \
            1,3,5,7,9,10,8,6,4,2 \
            endarray
            right)$






            share|improve this answer











            $endgroup$












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              3 Answers
              3






              active

              oldest

              votes








              3 Answers
              3






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              4












              $begingroup$

              cg = Compile[a, _Integer, 1, b, _Integer, 1, i, _Integer,
              Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
              CompilationTarget -> "WVM",
              RuntimeAttributes -> Listable,
              Parallelization -> True
              ];
              g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





              share|improve this answer











              $endgroup$












              • $begingroup$
                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                $endgroup$
                – Jerry
                Jan 18 at 10:01











              • $begingroup$
                Good point, I added the pattern after posting...
                $endgroup$
                – Henrik Schumacher
                Jan 18 at 10:10















              4












              $begingroup$

              cg = Compile[a, _Integer, 1, b, _Integer, 1, i, _Integer,
              Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
              CompilationTarget -> "WVM",
              RuntimeAttributes -> Listable,
              Parallelization -> True
              ];
              g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





              share|improve this answer











              $endgroup$












              • $begingroup$
                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                $endgroup$
                – Jerry
                Jan 18 at 10:01











              • $begingroup$
                Good point, I added the pattern after posting...
                $endgroup$
                – Henrik Schumacher
                Jan 18 at 10:10













              4












              4








              4





              $begingroup$

              cg = Compile[a, _Integer, 1, b, _Integer, 1, i, _Integer,
              Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
              CompilationTarget -> "WVM",
              RuntimeAttributes -> Listable,
              Parallelization -> True
              ];
              g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];





              share|improve this answer











              $endgroup$



              cg = Compile[a, _Integer, 1, b, _Integer, 1, i, _Integer,
              Join[a[[1 ;; Quotient[i + 1, 2]]], b[[-Quotient[i, 2] ;; -1]]],
              CompilationTarget -> "WVM",
              RuntimeAttributes -> Listable,
              Parallelization -> True
              ];
              g[n_Integer] := cg[Range[1, n + 1, 2], Range[n + Mod[n, 2], 2, -2], Range[2, n + 1]];






              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited Jan 18 at 10:10

























              answered Jan 18 at 9:28









              Henrik SchumacherHenrik Schumacher

              52.4k470147




              52.4k470147











              • $begingroup$
                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                $endgroup$
                – Jerry
                Jan 18 at 10:01











              • $begingroup$
                Good point, I added the pattern after posting...
                $endgroup$
                – Henrik Schumacher
                Jan 18 at 10:10
















              • $begingroup$
                there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
                $endgroup$
                – Jerry
                Jan 18 at 10:01











              • $begingroup$
                Good point, I added the pattern after posting...
                $endgroup$
                – Henrik Schumacher
                Jan 18 at 10:10















              $begingroup$
              there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
              $endgroup$
              – Jerry
              Jan 18 at 10:01





              $begingroup$
              there's a little bug with g[n_?Integer], use g[n_Integer] or g[n_?IntegerQ] instead.
              $endgroup$
              – Jerry
              Jan 18 at 10:01













              $begingroup$
              Good point, I added the pattern after posting...
              $endgroup$
              – Henrik Schumacher
              Jan 18 at 10:10




              $begingroup$
              Good point, I added the pattern after posting...
              $endgroup$
              – Henrik Schumacher
              Jan 18 at 10:10











              6












              $begingroup$

              ClearAll[f]
              f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
              TeXForm @ MatrixForm @ f[8]



              $left(
              beginarrayc
              1,2 \
              1,3,2 \
              1,3,4,2 \
              1,3,5,4,2 \
              1,3,5,6,4,2 \
              1,3,5,7,6,4,2 \
              1,3,5,7,8,6,4,2 \
              endarray
              right)$




              Also



              ClearAll[f2, f3]
              f2[n_Integer] := SortBy[Range@#, EvenQ, -# (-1 )^Mod[#, 2] &] & /@ Range[2, n]
              f3[n_] := Ordering[Transpose[-Mod[#, 2], -# (-1 )^Mod[#, 2] &@Range[#]]] & /@ Range[2, n]

              f[8] == f2[8] == f3[8]



              True







              share|improve this answer











              $endgroup$

















                6












                $begingroup$

                ClearAll[f]
                f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
                TeXForm @ MatrixForm @ f[8]



                $left(
                beginarrayc
                1,2 \
                1,3,2 \
                1,3,4,2 \
                1,3,5,4,2 \
                1,3,5,6,4,2 \
                1,3,5,7,6,4,2 \
                1,3,5,7,8,6,4,2 \
                endarray
                right)$




                Also



                ClearAll[f2, f3]
                f2[n_Integer] := SortBy[Range@#, EvenQ, -# (-1 )^Mod[#, 2] &] & /@ Range[2, n]
                f3[n_] := Ordering[Transpose[-Mod[#, 2], -# (-1 )^Mod[#, 2] &@Range[#]]] & /@ Range[2, n]

                f[8] == f2[8] == f3[8]



                True







                share|improve this answer











                $endgroup$















                  6












                  6








                  6





                  $begingroup$

                  ClearAll[f]
                  f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
                  TeXForm @ MatrixForm @ f[8]



                  $left(
                  beginarrayc
                  1,2 \
                  1,3,2 \
                  1,3,4,2 \
                  1,3,5,4,2 \
                  1,3,5,6,4,2 \
                  1,3,5,7,6,4,2 \
                  1,3,5,7,8,6,4,2 \
                  endarray
                  right)$




                  Also



                  ClearAll[f2, f3]
                  f2[n_Integer] := SortBy[Range@#, EvenQ, -# (-1 )^Mod[#, 2] &] & /@ Range[2, n]
                  f3[n_] := Ordering[Transpose[-Mod[#, 2], -# (-1 )^Mod[#, 2] &@Range[#]]] & /@ Range[2, n]

                  f[8] == f2[8] == f3[8]



                  True







                  share|improve this answer











                  $endgroup$



                  ClearAll[f]
                  f[n_Integer] := Join[Range[1, #, 2], Reverse[Range[2, #, 2]]] & /@ Range[2, n];
                  TeXForm @ MatrixForm @ f[8]



                  $left(
                  beginarrayc
                  1,2 \
                  1,3,2 \
                  1,3,4,2 \
                  1,3,5,4,2 \
                  1,3,5,6,4,2 \
                  1,3,5,7,6,4,2 \
                  1,3,5,7,8,6,4,2 \
                  endarray
                  right)$




                  Also



                  ClearAll[f2, f3]
                  f2[n_Integer] := SortBy[Range@#, EvenQ, -# (-1 )^Mod[#, 2] &] & /@ Range[2, n]
                  f3[n_] := Ordering[Transpose[-Mod[#, 2], -# (-1 )^Mod[#, 2] &@Range[#]]] & /@ Range[2, n]

                  f[8] == f2[8] == f3[8]



                  True








                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited Jan 18 at 8:27

























                  answered Jan 18 at 7:35









                  kglrkglr

                  182k10200413




                  182k10200413





















                      5












                      $begingroup$

                       fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest

                      fGetList[10] // MatrixForm // TeXForm


                      $
                      left(
                      beginarrayc
                      1,2 \
                      1,3,2 \
                      1,3,4,2 \
                      1,3,5,4,2 \
                      1,3,5,6,4,2 \
                      1,3,5,7,6,4,2 \
                      1,3,5,7,8,6,4,2 \
                      1,3,5,7,9,8,6,4,2 \
                      1,3,5,7,9,10,8,6,4,2 \
                      endarray
                      right)$



                      another version



                      fGetList2[n_?IntegerQ] := 
                      Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]

                      fGetList2[10] // MatrixForm // TeXForm


                      $left(
                      beginarrayc
                      1,2 \
                      1,3,2 \
                      1,3,4,2 \
                      1,3,5,4,2 \
                      1,3,5,6,4,2 \
                      1,3,5,7,6,4,2 \
                      1,3,5,7,8,6,4,2 \
                      1,3,5,7,9,8,6,4,2 \
                      1,3,5,7,9,10,8,6,4,2 \
                      endarray
                      right)$






                      share|improve this answer











                      $endgroup$

















                        5












                        $begingroup$

                         fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest

                        fGetList[10] // MatrixForm // TeXForm


                        $
                        left(
                        beginarrayc
                        1,2 \
                        1,3,2 \
                        1,3,4,2 \
                        1,3,5,4,2 \
                        1,3,5,6,4,2 \
                        1,3,5,7,6,4,2 \
                        1,3,5,7,8,6,4,2 \
                        1,3,5,7,9,8,6,4,2 \
                        1,3,5,7,9,10,8,6,4,2 \
                        endarray
                        right)$



                        another version



                        fGetList2[n_?IntegerQ] := 
                        Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]

                        fGetList2[10] // MatrixForm // TeXForm


                        $left(
                        beginarrayc
                        1,2 \
                        1,3,2 \
                        1,3,4,2 \
                        1,3,5,4,2 \
                        1,3,5,6,4,2 \
                        1,3,5,7,6,4,2 \
                        1,3,5,7,8,6,4,2 \
                        1,3,5,7,9,8,6,4,2 \
                        1,3,5,7,9,10,8,6,4,2 \
                        endarray
                        right)$






                        share|improve this answer











                        $endgroup$















                          5












                          5








                          5





                          $begingroup$

                           fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest

                          fGetList[10] // MatrixForm // TeXForm


                          $
                          left(
                          beginarrayc
                          1,2 \
                          1,3,2 \
                          1,3,4,2 \
                          1,3,5,4,2 \
                          1,3,5,6,4,2 \
                          1,3,5,7,6,4,2 \
                          1,3,5,7,8,6,4,2 \
                          1,3,5,7,9,8,6,4,2 \
                          1,3,5,7,9,10,8,6,4,2 \
                          endarray
                          right)$



                          another version



                          fGetList2[n_?IntegerQ] := 
                          Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]

                          fGetList2[10] // MatrixForm // TeXForm


                          $left(
                          beginarrayc
                          1,2 \
                          1,3,2 \
                          1,3,4,2 \
                          1,3,5,4,2 \
                          1,3,5,6,4,2 \
                          1,3,5,7,6,4,2 \
                          1,3,5,7,8,6,4,2 \
                          1,3,5,7,9,8,6,4,2 \
                          1,3,5,7,9,10,8,6,4,2 \
                          endarray
                          right)$






                          share|improve this answer











                          $endgroup$



                           fGetList[n_]:= (Select[Range[#], OddQ]~Join~Reverse@Select[Range[#], EvenQ]) & /@Range[n] // Rest

                          fGetList[10] // MatrixForm // TeXForm


                          $
                          left(
                          beginarrayc
                          1,2 \
                          1,3,2 \
                          1,3,4,2 \
                          1,3,5,4,2 \
                          1,3,5,6,4,2 \
                          1,3,5,7,6,4,2 \
                          1,3,5,7,8,6,4,2 \
                          1,3,5,7,9,8,6,4,2 \
                          1,3,5,7,9,10,8,6,4,2 \
                          endarray
                          right)$



                          another version



                          fGetList2[n_?IntegerQ] := 
                          Flatten@MapAt[Reverse, GatherBy[Range[#], OddQ], 2] & /@ Range[2, n]

                          fGetList2[10] // MatrixForm // TeXForm


                          $left(
                          beginarrayc
                          1,2 \
                          1,3,2 \
                          1,3,4,2 \
                          1,3,5,4,2 \
                          1,3,5,6,4,2 \
                          1,3,5,7,6,4,2 \
                          1,3,5,7,8,6,4,2 \
                          1,3,5,7,9,8,6,4,2 \
                          1,3,5,7,9,10,8,6,4,2 \
                          endarray
                          right)$







                          share|improve this answer














                          share|improve this answer



                          share|improve this answer








                          edited Jan 18 at 7:54

























                          answered Jan 18 at 7:35









                          JerryJerry

                          1,380212




                          1,380212



























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