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

0,4

Links

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

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 *)

Crossrefs

Column k=8 of A250261.

Sequence in context: A004859 A237345 A024655 * A273476 A278943 A303167

Adjacent sequences: A250261 A250262 A250263 * A250265 A250266 A250267

Keyword

nonn

Author

Alois P. Heinz, Nov 15 2014

Status

approved