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A250262 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 6).

%I A250262 #12 Sep 03 2021 01:51:26
%S A250262 1,1,1,2,3,4,5,6,41,208,711,1970,4741,10284,123397,1041224,5690415,
%T A250262 24359248,87922385,278723178,4777712981,56439873880,424119250083,
%U A250262 2456329637366,11821181689417,49308397822776,1098781192727401,16688667550625072,159609583197355203
%N A250262 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 1 (mod 6).
%H A250262 Alois P. Heinz, <a href="/A250262/b250262.txt">Table of n, a(n) for n = 0..500</a>
%p A250262 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A250262      `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 6)), j=1..u),
%p A250262                add(b(u+j-1, o-j, irem(t+1, 6)), j=1..o)))
%p A250262     end:
%p A250262 a:= n-> b(0, n, 0):
%p A250262 seq(a(n), n=0..35);
%t A250262 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, 6]], {j, 1, u}], Sum[b[u + j - 1, o - j, Mod[t + 1, 6]], {j, 1, o}]]];
%t A250262 a[n_] := b[0, n, 0];
%t A250262 Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Jul 22 2019, after _Alois P. Heinz_ *)
%Y A250262 Column k=6 of A250261.
%K A250262 nonn
%O A250262 0,4
%A A250262 _Alois P. Heinz_, Nov 15 2014