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A177519 Number of permutations of 1..n avoiding adjacent step pattern up, down, down, up.

%I A177519 #26 Apr 20 2022 09:11:34
%S A177519 1,1,2,6,24,109,588,3654,26125,209863,1876502,18441367,197776850,
%T A177519 2297242583,28739304385,385195455471,5507210188401,83657067537498,
%U A177519 1345556172013026,22844387886649418,408258252653717337,7660885499702743124,150600621665021781932
%N A177519 Number of permutations of 1..n avoiding adjacent step pattern up, down, down, up.
%H A177519 Alois P. Heinz, <a href="/A177519/b177519.txt">Table of n, a(n) for n = 0..458</a>
%F A177519 a(n) ~ c * d^n * n!, where d = 0.89356257576899599804435763285311831354458355576519..., c = 1.593348415562339201282264582915828860634166516332738... . - _Vaclav Kotesovec_, Aug 29 2014
%p A177519 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A177519       `if`(t<3, add(b(u+j-1, o-j, 1), j=1..o), 0)+
%p A177519       add(b(u-j, o+j-1, `if`(t in [0,3], 0, t+1)), j=1..u))
%p A177519     end:
%p A177519 a:= n-> b(n, 0, 0):
%p A177519 seq(a(n), n=0..30);  # _Alois P. Heinz_, Oct 07 2013
%t A177519 b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1, If[t < 3,
%t A177519      Sum[b[u + j - 1, o - j, 1], {j, 1, o}], 0] +
%t A177519      Sum[b[u - j, o + j - 1, If[MemberQ[{0, 3}, t], 0, t+1]], {j, 1, u}]];
%t A177519 a[n_] := b[n, 0, 0];
%t A177519 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 20 2022, after _Alois P. Heinz_ *)
%Y A177519 Column k=0 of A230695.
%Y A177519 Column k=9 of A242784.
%K A177519 nonn
%O A177519 0,3
%A A177519 _R. H. Hardin_, May 10 2010
%E A177519 a(17)-a(22) from _Alois P. Heinz_, Oct 07 2013
%E A177519 a(0)=1 from _Alois P. Heinz_, Apr 20 2022