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A177543 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, down.

%I A177543 #16 Apr 19 2022 06:28:32
%S A177543 1,1,2,6,24,120,720,4768,35968,312064,3004160,31764480,365798400,
%T A177543 4555499520,61232590848,882227765248,13547017240576,221038858829824,
%U A177543 3818608204709888,69637156745773056,1336921845773107200,26947721453843251200,569023211226594803712
%N A177543 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, down.
%H A177543 Alois P. Heinz, <a href="/A177543/b177543.txt">Table of n, a(n) for n = 0..175</a>
%F A177543 a(n) ~ c * d^n * n!, where d = 0.9598365530271216889440240044515..., c = 1.2474579024498809739499621681... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177543 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177543       add(b(u-j, o+j-1, [1, 3, 1, 5, 1, 7][t]), j=1..u)+
%p A177543       add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 2][t]), j=1..o)))
%p A177543     end:
%p A177543 a:= n-> b(n, 0, 1):
%p A177543 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 24 2013
%t A177543 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177543      Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 1, 7}[[t]]], {j, 1, u}] +
%t A177543      Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 2}[[t]]], {j, 1, o}]]];
%t A177543 a[n_] := b[n, 0, 1];
%t A177543 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177543 Column k=42 of A242784.
%K A177543 nonn
%O A177543 0,3
%A A177543 _R. H. Hardin_, May 10 2010
%E A177543 a(17)-a(22) from _Alois P. Heinz_, Oct 24 2013