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A177528 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down.

%I A177528 #20 Apr 19 2022 11:02:11
%S A177528 1,1,2,6,24,120,685,4550,34440,292320,2746800,28402925,320224500,
%T A177528 3909695400,51396618000,723952593000,10876269801125,173607227828250,
%U A177528 2934111079914750,52343975053683000,982945842995115000,19381240178451775625,400347201716808478750
%N A177528 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down.
%H A177528 Alois P. Heinz, <a href="/A177528/b177528.txt">Table of n, a(n) for n = 0..454</a>
%F A177528 a(n) ~ c * d^n * n!, where d = 0.93892752514028508419326638408810575968441290684141..., c = 1.4248368339815259677105814450156343177071690245... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177528 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
%p A177528       add(b(u-j, o+j-1, [1, 3, 1, 5, 6][t]), j=1..u)+
%p A177528       add(b(u+j-1, o-j, [2, 2, 4, 2, 4][t]), j=1..o)))
%p A177528     end:
%p A177528 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177528 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177528 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t A177528      Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 6}[[t]]], {j, 1, u}] +
%t A177528      Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 4}[[t]]], {j, 1, o}]]];
%t A177528 a[n_] := b[n, 0, 1];
%t A177528 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177528 Columns k=20,26 of A242784.
%Y A177528 Cf. A317639.
%K A177528 nonn
%O A177528 0,3
%A A177528 _R. H. Hardin_, May 10 2010
%E A177528 a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013