A338765 Number of permutations p of [n] such that | |p(i) - p(i-1)| - |p(i+1) - p(i)| | <= 1.

1, 1, 2, 6, 18, 38, 76, 162, 330, 650, 1272, 2586, 5262, 10506, 20856, 41928, 83684, 165800, 329310, 653614, 1303388, 2584660, 5139580, 10210912, 20288128, 40224174, 79824572, 158316222, 314272812

Offset: 0

Author

Alois P. Heinz, Nov 07 2020

Keywords

• nonn
• more

Links

• Wikipedia, Permutation

Crossrefs

Cf. A295370, A338766.

Programs

Maple

b:= proc(s, x, y) option remember; `if`(s={}, 1, add(
      `if`(x=0 or y=0 or abs(abs(x-y)-abs(y-j))<=1,
         b(s minus {j}, y, j), 0), j=s))
    end:
a:= n-> b({$1..n}, 0$2):
seq(a(n), n=0..15);

Mathematica

b[s_, x_, y_] := b[s, x, y] = If[s == {}, 1, Sum[
     If[x == 0 || y == 0 || Abs[Abs[x - y] - Abs[y - j]] <= 1,
     b[s ~Complement~ {j}, y, j], 0], {j, s}]];
a[n_] := b[Range[n], 0, 0];
a /@ Range[0, 15] (* Jean-François Alcover, Apr 26 2021, after Alois P. Heinz *)