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A177540 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, down.

%I A177540 #14 Apr 19 2022 11:01:58
%S A177540 1,1,2,6,24,120,720,4908,38208,334368,3248640,34774112,405758208,
%T A177540 5129918808,69849531936,1018876044528,15854497560576,262116761475488,
%U A177540 4588408779868800,84784281517177940,1649073291620014880,33678805727832427224,720569710852319474016
%N A177540 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, down.
%H A177540 Alois P. Heinz, <a href="/A177540/b177540.txt">Table of n, a(n) for n = 0..175</a>
%F A177540 a(n) ~ c * d^n * n!, where d = 0.97251576612005359341988641793523250275..., c = 1.18354011206219905745522624899424386... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177540 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177540       add(b(u-j, o+j-1, [1, 3, 4, 1, 3, 7][t]), j=1..u)+
%p A177540       add(b(u+j-1, o-j, [2, 2, 2, 5, 6, 2][t]), j=1..o)))
%p A177540     end:
%p A177540 a:= n-> b(n, 0, 1):
%p A177540 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 24 2013
%t A177540 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177540      Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3, 7}[[t]]], {j, 1, u}] +
%t A177540      Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6, 2}[[t]]], {j, 1, o}]]];
%t A177540 a[n_] := b[n, 0, 1];
%t A177540 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177540 Column k=38 of A242784.
%K A177540 nonn
%O A177540 0,3
%A A177540 _R. H. Hardin_, May 10 2010
%E A177540 a(17)-a(22) from _Alois P. Heinz_, Oct 24 2013