cp's OEIS Frontend

A177545 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, down.

%I A177545 #17 Apr 19 2022 07:25:57
%S A177545 1,1,2,6,24,120,720,4929,38544,338904,3309120,35521200,415704960,
%T A177545 5271197205,71977504692,1053008012790,16431803844480,272435676775200,
%U A177545 4782657847248000,88624515772410633,1728678866577622920,35404942557640528620,759655818204633900000
%N A177545 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, down, down.
%H A177545 Alois P. Heinz, <a href="/A177545/b177545.txt">Table of n, a(n) for n = 0..190</a>
%F A177545 a(n) ~ c * d^n * n!, where d = 0.9752820884477652193970997660966130503977714987577677..., c = 1.1721546677937404500752065441275892023818795500231... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177545 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177545       add(b(u-j, o+j-1, [1, 3, 1, 3, 6, 7][t]), j=1..u)+
%p A177545       add(b(u+j-1, o-j, [2, 2, 4, 5, 2, 4][t]), j=1..o)))
%p A177545     end:
%p A177545 a:= n-> b(n, 0, 1):
%p A177545 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 22 2013
%t A177545 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177545      Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 6, 7}[[t]]], {j, 1, u}] +
%t A177545      Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 2, 4}[[t]]], {j, 1, o}]]];
%t A177545 a[n_] := b[n, 0, 1];
%t A177545 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177545 Columns k=44,50 of A242784.
%K A177545 nonn
%O A177545 0,3
%A A177545 _R. H. Hardin_, May 10 2010
%E A177545 a(17)-a(22) from _Alois P. Heinz_, Oct 22 2013