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A177526 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down.

%I A177526 #16 Apr 19 2022 11:02:42
%S A177526 1,1,2,6,24,120,680,4480,33600,285434,2684680,27812170,313926560,
%T A177526 3842611240,50625902600,714873188122,10764733339179,172258243070682,
%U A177526 2918333808555034,52191694000877878,982479378895814520,19419959862935129834,402131210857811703926
%N A177526 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down.
%H A177526 Alois P. Heinz, <a href="/A177526/b177526.txt">Table of n, a(n) for n = 0..170</a>
%F A177526 a(n) ~ c * d^n * n!, where d = 0.94123983763344712685016041467..., c = 1.3558011859159420827133973526... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177526 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
%p A177526       add(b(u-j, o+j-1, [1, 3, 4, 1, 6][t]), j=1..u)+
%p A177526       add(b(u+j-1, o-j, [2, 2, 2, 5, 2][t]), j=1..o)))
%p A177526     end:
%p A177526 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177526 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177526 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t A177526      Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 6}[[t]]], {j, 1, u}] +
%t A177526      Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2}[[t]]], {j, 1, o}]]];
%t A177526 a[n_] := b[n, 0, 1];
%t A177526 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177526 Columns k=18,22 of A242784.
%K A177526 nonn
%O A177526 0,3
%A A177526 _R. H. Hardin_, May 10 2010
%E A177526 a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013