A338766 Number of permutations p of [n] such that | |p(i) - p(i-1)| - |p(i+1) - p(i)| | = 1.

1, 1, 2, 4, 16, 20, 32, 56, 148, 136, 186, 328, 894, 868, 1196, 1896, 5210, 4936, 6716, 11264, 30046, 28168, 38892, 63272, 169900, 161848, 218944, 367616, 966010, 909192, 1240738, 2100064, 5422442, 5161412, 7027750, 11910404

Offset: 0

Author

Alois P. Heinz, Nov 07 2020

Keywords

• nonn
• more

Links

• Wikipedia, Permutation

Crossrefs

Cf. A338765.

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..20);

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, 20] (* Jean-François Alcover, Apr 26 2021, after Alois P. Heinz *)