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A177529 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up.

%I A177529 #17 Apr 19 2022 11:08:26
%S A177529 1,1,2,6,24,120,659,4186,31457,264834,2465550,25334981,283322383,
%T A177529 3430384284,44803783445,626719448981,9347396890481,148174002240074,
%U A177529 2486833885400060,44052337160572208,821495697573151302,16085109561896603059,329939476998354570978
%N A177529 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up.
%H A177529 Alois P. Heinz, <a href="/A177529/b177529.txt">Table of n, a(n) for n = 0..200</a>
%F A177529 a(n) ~ c * d^n * n!, where d = 0.9323832531422843725281328190771918152..., c = 1.369593476632786981162993013559816... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177529 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
%p A177529       add(b(u-j, o+j-1, [1, 3, 1, 5, 1][t]), j=1..u)+
%p A177529       add(b(u+j-1, o-j, [2, 2, 4, 2, 6][t]), j=1..o)))
%p A177529     end:
%p A177529 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177529 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177529 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t A177529      Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 1}[[t]]], {j, 1, u}] +
%t A177529      Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6}[[t]]], {j, 1, o}]]];
%t A177529 a[n_] := b[n, 0, 1];
%t A177529 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177529 Column k=21 of A242784.
%K A177529 nonn
%O A177529 0,3
%A A177529 _R. H. Hardin_, May 10 2010