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A177544 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, up.

%I A177544 #16 Apr 19 2022 07:25:36
%S A177544 1,1,2,6,24,120,720,4885,37840,329400,3182400,33778800,391590750,
%T A177544 4915323791,66442003448,962278914330,14866633343040,244014015391725,
%U A177544 4240899164064012,77799960323395327,1502369690026049320,30462229695574890900,647071778569768101485
%N A177544 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, up, up.
%H A177544 Alois P. Heinz, <a href="/A177544/b177544.txt">Table of n, a(n) for n = 0..200</a>
%F A177544 a(n) ~ c * d^n * n!, where d = 0.96553264441829855042601163560012935129948..., c = 1.245410138868090155003662557978590938375... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177544 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177544       add(b(u-j, o+j-1, [1, 3, 1, 5, 1, 5][t]), j=1..u)+
%p A177544       add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 7][t]), j=1..o)))
%p A177544     end:
%p A177544 a:= n-> b(n, 0, 1):
%p A177544 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 30 2013
%t A177544 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177544      Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 1, 5}[[t]]], {j, 1, u}] +
%t A177544      Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 7}[[t]]], {j, 1, o}]]];
%t A177544 a[n_] := b[n, 0, 1];
%t A177544 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177544 Columns k=43,53 of A242784.
%K A177544 nonn
%O A177544 0,3
%A A177544 _R. H. Hardin_, May 10 2010
%E A177544 a(17)-a(22) from _Alois P. Heinz_, Oct 30 2013