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A177522 Number of permutations of 1..n avoiding adjacent step pattern up, up, down, down.

%I A177522 #20 Apr 20 2022 09:03:37
%S A177522 1,1,2,6,24,114,648,4284,32256,273616,2578352,26725776,302273664,
%T A177522 3703441104,48865510848,690823736064,10417318281216,166907223390976,
%U A177522 2831507368842752,50703852290781696,955742450175919104,18916030525704006144,392213482250102734848
%N A177522 Number of permutations of 1..n avoiding adjacent step pattern up, up, down, down.
%H A177522 Alois P. Heinz, <a href="/A177522/b177522.txt">Table of n, a(n) for n = 0..454</a>
%F A177522 a(n) ~ c * d^n * n!, where d = 0.942475018599378010857210678432739023432859616925664352..., c = 1.284751954587372264742653082845227922651555734159194626... . - _Vaclav Kotesovec_, Aug 29 2014
%p A177522 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A177522       add(b(u+j-1, o-j, `if`(t in [0, 3], 1, 2)), j=1..o)+`if`(t<3,
%p A177522       add(b(u-j, o+j-1, `if`(t=2, 3, 0)), j=1..u), 0))
%p A177522     end:
%p A177522 a:= n-> b(n, 0, 0):
%p A177522 seq(a(n), n=0..30);  # _Alois P. Heinz_, Oct 07 2013
%t A177522 b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,
%t A177522      Sum[b[u+j-1, o-j, If[MemberQ[{0, 3}, t], 1, 2]], {j, 1, o}] + If[t<3,
%t A177522      Sum[b[u-j, o+j-1, If[t == 2, 3, 0]], {j, 1, u}], 0]];
%t A177522 a[n_] := b[n, 0, 0];
%t A177522 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 20 2022, after _Alois P. Heinz_ *)
%Y A177522 Column k=12 of A242784.
%K A177522 nonn
%O A177522 0,3
%A A177522 _R. H. Hardin_, May 10 2010
%E A177522 a(17)-a(22) from _Alois P. Heinz_, Oct 07 2013
%E A177522 a(0)=1 from _Alois P. Heinz_, Apr 20 2022