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%I #16 Apr 19 2022 11:33:01
%S 1,1,2,6,24,120,701,4774,37128,326089,3184221,34191983,400308461,
%T 5076257396,69329710171,1014612340743,15838898430094,262706269352374,
%U 4613506518038420,85520547931176984,1668736482655334275,34189755475407632542,733851215342599413848
%N Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, up.
%H Alois P. Heinz, <a href="/A177532/b177532.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) ~ c * d^n * n!, where d = 0.975638124670183802889377522566191208591041394..., c = 1.123281860028517266849117754708517961017398615... . - _Vaclav Kotesovec_, Jan 17 2015
%p b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
%p add(b(u-j, o+j-1, [1, 1, 4, 1, 1][t]), j=1..u)+
%p add(b(u+j-1, o-j, [2, 3, 3, 5, 6][t]), j=1..o)))
%p end:
%p a:= n-> b(n, 0, 1):
%p seq(a(n), n=0..25); # _Alois P. Heinz_, Oct 21 2013
%t b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t Sum[b[u - j, o + j - 1, {1, 1, 4, 1, 1}[[t]]], {j, 1, u}] +
%t Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 6}[[t]]], {j, 1, o}]]];
%t a[n_] := b[n, 0, 1];
%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y Column k=27 of A242784.
%K nonn
%O 0,3
%A _R. H. Hardin_, May 10 2010
%E a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013
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