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A177536 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, down.

%I A177536 #14 Apr 19 2022 11:35:32
%S A177536 1,1,2,6,24,120,720,4962,39072,346032,3404160,36853442,435133488,
%T A177536 5566069380,76676528112,1131700250442,17817052536384,298034349244128,
%U A177536 5278625637077376,98686282426953080,1942087278998014400,40130098178033129036,868710371909527352944
%N A177536 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up, down.
%H A177536 Alois P. Heinz, <a href="/A177536/b177536.txt">Table of n, a(n) for n = 0..175</a>
%F A177536 a(n) ~ c * d^n * n!, where d = 0.983970585738736307495769238852152954976022611246..., c = 1.1028129540167952253429967393297373345979852081... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177536 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177536       add(b(u-j, o+j-1, [1, 3, 4, 5, 1, 7][t]), j=1..u)+
%p A177536       add(b(u+j-1, o-j, [2, 2, 2, 2, 6, 2][t]), j=1..o)))
%p A177536     end:
%p A177536 a:= n-> b(n, 0, 1):
%p A177536 seq(a(n), n=0..25);   # _Alois P. Heinz_, Oct 24 2013
%t A177536 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177536      Sum[b[u - j, o + j - 1, {1, 3, 4, 5, 1, 7}[[t]]], {j, 1, u}] +
%t A177536      Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 6, 2}[[t]]], {j, 1, o}]]];
%t A177536 a[n_] := b[n, 0, 1];
%t A177536 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177536 Column k=34,46 of A242784.
%K A177536 nonn
%O A177536 0,3
%A A177536 _R. H. Hardin_, May 10 2010
%E A177536 a(17)-a(22) from _Alois P. Heinz_, Oct 24 2013