A250262 - OEIS

%I #12 Sep 03 2021 01:51:26

%S 1,1,1,2,3,4,5,6,41,208,711,1970,4741,10284,123397,1041224,5690415,

%T 24359248,87922385,278723178,4777712981,56439873880,424119250083,

%U 2456329637366,11821181689417,49308397822776,1098781192727401,16688667550625072,159609583197355203

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

%H Alois P. Heinz, <a href="/A250262/b250262.txt">Table of n, a(n) for n = 0..500</a>

%p b:= proc(u, o, t) option remember; `if`(u+o=0, 1,

%p      `if`(t=1, add(b(u-j, o+j-1, irem(t+1, 6)), j=1..u),

%p                add(b(u+j-1, o-j, irem(t+1, 6)), j=1..o)))

%p     end:

%p a:= n-> b(0, n, 0):

%p seq(a(n), n=0..35);

%t 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 a[n_] := b[0, n, 0];

%t Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Jul 22 2019, after _Alois P. Heinz_ *)

%Y Column k=6 of A250261.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Nov 15 2014