A250264 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 8).

1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 71, 430, 1749, 5708, 16003, 40026, 91505, 194464, 3111409, 32514338, 220345299, 1161515620, 5117035637, 19624019910, 67294308247, 210311057024, 4860499987799, 72178664783758, 684803123126277, 4985006104393196, 29947298627248915

Offset: 0

Author

Alois P. Heinz, Nov 15 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Column k=8 of A250261.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
     `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 8)), j=1..u),
               add(b(u+j-1, o-j, irem(t+1, 8)), j=1..o)))
    end:
a:= n-> b(0, n, 0):
seq(a(n), n=0..35);

Mathematica

b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, If[t == 1, Sum[b[u - j, o + j - 1, Mod[t + 1, 8]], {j, 1, u}], Sum[b[u + j - 1, o - j, Mod[t + 1, 8]], {j, 1, o}]]];
a[n_] := b[0, n, 0];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jul 22 2019, after Alois P. Heinz *)