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A177520 Number of permutations of 1..n avoiding adjacent step pattern up, down, up, down.

%I A177520 #22 Apr 20 2022 09:15:22
%S A177520 1,1,2,6,24,104,528,3296,23168,179712,1573632,15207424,158880768,
%T A177520 1801996288,22088716288,289379395584,4040899657728,60045059489792,
%U A177520 944460646318080,15670973219667968,273813250221277184,5024207327266603008,96554813072964845568
%N A177520 Number of permutations of 1..n avoiding adjacent step pattern up, down, up, down.
%H A177520 Alois P. Heinz, <a href="/A177520/b177520.txt">Table of n, a(n) for n = 0..460</a>
%F A177520 a(n) ~ c * d^n * n!, where d = 0.87361286073825385348141673848..., c = 1.678751353034864037734331900009... . - _Vaclav Kotesovec_, Aug 28 2014
%p A177520 b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
%p A177520       add(b(u+j-1, o-j, `if`(t=2, 3, 1)), j=1..o) +`if`(t<3,
%p A177520       add(b(u-j, o+j-1, `if`(t=1, 2, 0)), j=1..u), 0))
%p A177520     end:
%p A177520 a:= n-> b(n, 0, 0):
%p A177520 seq(a(n), n=0..30);  # _Alois P. Heinz_, Oct 07 2013
%t A177520 b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,
%t A177520      Sum[b[u + j - 1, o - j, If[t == 2, 3, 1]], {j, 1, o}] + If[t < 3,
%t A177520      Sum[b[u - j, o + j - 1, If[t == 1, 2, 0]], {j, 1, u}], 0]];
%t A177520 a[n_] := b[n, 0, 0];
%t A177520 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, Apr 20 2022, after _Alois P. Heinz_ *)
%Y A177520 Column k=0 of A230797.
%Y A177520 Column k=10 of A242784.
%K A177520 nonn
%O A177520 0,3
%A A177520 _R. H. Hardin_, May 10 2010
%E A177520 a(17)-a(22) from _Alois P. Heinz_, Oct 07 2013