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A177527 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up.

%I A177527 #16 Apr 19 2022 11:08:12
%S A177527 1,1,2,6,24,120,694,4676,35952,310464,2984176,31536583,363591384,
%T A177527 4541789148,61089594448,880428095803,13534614549829,221066397540186,
%U A177527 3823205871530350,69792946997645295,1341134146478847104,27059669661295560098,571973335506443017436
%N A177527 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up.
%H A177527 Alois P. Heinz, <a href="/A177527/b177527.txt">Table of n, a(n) for n = 0..170</a>
%F A177527 a(n) ~ c * d^n * n!, where d = 0.96079505301634594056671142147783512755736606..., c = 1.2266835832918378326758739778897107143678546... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177527 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
%p A177527       add(b(u-j, o+j-1, [1,3,4,1,3][t]), j=1..u)+
%p A177527       add(b(u+j-1, o-j, [2,2,2,5,6][t]), j=1..o)))
%p A177527     end:
%p A177527 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177527 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177527 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t A177527      Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3}[[t]]], {j, 1, u}] +
%t A177527      Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6}[[t]]], {j, 1, o}]]];
%t A177527 a[n_] := b[n, 0, 1];
%t A177527 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177527 Columns k=19,25 of A242784.
%K A177527 nonn
%O A177527 0,3
%A A177527 _R. H. Hardin_, May 10 2010
%E A177527 a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013