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A177525 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up.

%I A177525 #16 Apr 19 2022 11:02:20
%S A177525 1,1,2,6,24,120,701,4774,37128,324576,3153961,33709743,393044544,
%T A177525 4964774568,67536381485,984328864872,15302821821071,252773481889854,
%U A177525 4420945845050347,81616873102658977,1586065426493434829,32363206963164145993,691807691094619216393
%N A177525 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, up.
%H A177525 Alois P. Heinz, <a href="/A177525/b177525.txt">Table of n, a(n) for n = 0..170</a>
%F A177525 a(n) ~ c * d^n * n!, where d = 0.971652908773770631708593889167049741726729704564696579529716779..., c = 1.15870633318154171410681190800508780736090448111042904596... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177525 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
%p A177525       add(b(u-j, o+j-1, [1,3,4,5,1][t]), j=1..u)+
%p A177525       add(b(u+j-1, o-j, [2,2,2,2,6][t]), j=1..o)))
%p A177525     end:
%p A177525 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177525 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177525 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t A177525      Sum[b[u - j, o + j - 1, {1, 3, 4, 5, 1}[[t]]], {j, 1, u}] +
%t A177525      Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 6}[[t]]], {j, 1, o}]]];
%t A177525 a[n_] := b[n, 0, 1];
%t A177525 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177525 Column k=17 of A242784.
%K A177525 nonn
%O A177525 0,3
%A A177525 _R. H. Hardin_, May 10 2010
%E A177525 a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013