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A177530 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up.

%I A177530 #15 Apr 19 2022 11:32:42
%S A177530 1,1,2,6,24,120,706,4844,37968,334656,3278896,35330098,415289184,
%T A177530 5288377848,72522052240,1065579141202,16700472769061,278099720959114,
%U A177530 4903387952699182,91258390273541562,1787828412527348984,36776310494510881628,792526608079806841508
%N A177530 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up.
%H A177530 Alois P. Heinz, <a href="/A177530/b177530.txt">Table of n, a(n) for n = 0..200</a>
%F A177530 a(n) ~ c * d^n * n!, where d = 0.9795419074893388679910049642242424087370823270695747551625158..., c = 1.111068410182136129001099552719852410280865324840041630689... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177530 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
%p A177530       add(b(u-j, o+j-1, [1, 3, 1, 3, 3][t]), j=1..u)+
%p A177530       add(b(u+j-1, o-j, [2, 2, 4, 5, 6][t]), j=1..o)))
%p A177530     end:
%p A177530 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177530 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177530 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t A177530      Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 3}[[t]]], {j, 1, u}] +
%t A177530      Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 6}[[t]]], {j, 1, o}]]];
%t A177530 a[n_] := b[n, 0, 1];
%t A177530 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177530 Columns k=23,29 of A242784.
%K A177530 nonn
%O A177530 0,3
%A A177530 _R. H. Hardin_, May 10 2010
%E A177530 a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013