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A177539 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, up.

%I A177539 #14 Apr 19 2022 11:01:41
%S A177539 1,1,2,6,24,120,720,4859,37424,323784,3107520,32749200,376929246,
%T A177539 4698101279,63058148792,906829731450,13911580276800,226738605155619,
%U A177539 3912973221007668,71280397766349665,1366816300552776920,27519285653572655340,580456044040809459821
%N A177539 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, up.
%H A177539 Alois P. Heinz, <a href="/A177539/b177539.txt">Table of n, a(n) for n = 0..175</a>
%F A177539 a(n) ~ c * d^n * n!, where d = 0.958757960478580745672487123002941621817..., c = 1.30438280919882137519668832091857761... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177539 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177539       add(b(u-j, o+j-1, [1, 3, 4, 1, 6, 4][t]), j=1..u)+
%p A177539       add(b(u+j-1, o-j, [2, 2, 2, 5, 2, 7][t]), j=1..o)))
%p A177539     end:
%p A177539 a:= n-> b(n, 0, 1):
%p A177539 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 24 2013
%t A177539 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177539      Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 6, 4}[[t]]], {j, 1, u}] +
%t A177539      Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2, 7}[[t]]], {j, 1, o}]]];
%t A177539 a[n_] := b[n, 0, 1];
%t A177539 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177539 Columns k=37,41 of A242784.
%K A177539 nonn
%O A177539 0,3
%A A177539 _R. H. Hardin_, May 10 2010
%E A177539 a(17)-a(22) from _Alois P. Heinz_, Oct 24 2013