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A177547 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up, up.

%I A177547 #16 Apr 19 2022 07:26:30
%S A177547 1,1,2,6,24,120,720,5020,40000,358560,3571200,39124800,467612575,
%T A177547 6054492822,84421683166,1261227594360,20098408531680,340297488208325,
%U A177547 6100696794591542,115446620042888642,2299637587367422120,48097983978364729800,1053895947990450296810
%N A177547 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, up, up, up.
%H A177547 Alois P. Heinz, <a href="/A177547/b177547.txt">Table of n, a(n) for n = 0..175</a>
%F A177547 a(n) ~ c * d^n * n!, where d = 0.995974410535227680608696027123957375635061175769113923461462667..., c = 1.0246396933863574062731686342310661124393526441879248790690509... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177547 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177547       add(b(u-j, o+j-1, [1, 3, 1, 3, 3, 3][t]), j=1..u)+
%p A177547       add(b(u+j-1, o-j, [2, 2, 4, 5, 6, 7][t]), j=1..o)))
%p A177547     end:
%p A177547 a:= n-> b(n, 0, 1):
%p A177547 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 23 2013
%t A177547 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177547      Sum[b[u - j, o + j - 1, {1, 3, 1, 3, 3, 3}[[t]]], {j, 1, u}] +
%t A177547      Sum[b[u + j - 1, o - j, {2, 2, 4, 5, 6, 7}[[t]]], {j, 1, o}]]];
%t A177547 a[n_] := b[n, 0, 1];
%t A177547 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177547 Columns k=47,61 of A242784.
%K A177547 nonn
%O A177547 0,3
%A A177547 _R. H. Hardin_, May 10 2010
%E A177547 a(17)-a(22) from _Alois P. Heinz_, Oct 23 2013