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

%I A250264 #12 Sep 03 2021 01:51:33
%S A250264 1,1,1,2,3,4,5,6,7,8,71,430,1749,5708,16003,40026,91505,194464,
%T A250264 3111409,32514338,220345299,1161515620,5117035637,19624019910,
%U A250264 67294308247,210311057024,4860499987799,72178664783758,684803123126277,4985006104393196,29947298627248915
%N A250264 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 8).
%H A250264 Alois P. Heinz, <a href="/A250264/b250264.txt">Table of n, a(n) for n = 0..500</a>
%p A250264 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A250264      `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 8)), j=1..u),
%p A250264                add(b(u+j-1, o-j, irem(t+1, 8)), j=1..o)))
%p A250264     end:
%p A250264 a:= n-> b(0, n, 0):
%p A250264 seq(a(n), n=0..35);
%t A250264 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}]]];
%t A250264 a[n_] := b[0, n, 0];
%t A250264 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Jul 22 2019, after _Alois P. Heinz_ *)
%Y A250264 Column k=8 of A250261.
%K A250264 nonn
%O A250264 0,4
%A A250264 _Alois P. Heinz_, Nov 15 2014