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A177541 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, up.

%I A177541 #17 Apr 19 2022 15:04:25
%S A177541 1,1,2,6,24,120,720,4990,39520,352080,3484800,37936800,450606300,
%T A177541 5797965980,80341280840,1192794269400,18889568419200,317838157969125,
%U A177541 5662578565559400,106488682710940108,2107992477960872320,43815112964794432080,954074378001971825930
%N A177541 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, up, up.
%H A177541 Alois P. Heinz, <a href="/A177541/b177541.txt">Table of n, a(n) for n = 0..150</a>
%F A177541 a(n) ~ c * d^n * n!, where d = 0.98977300089321592191180343193285102663621683..., c = 1.06422234334396404091033045795479059186356... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177541 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o=0, 1,
%p A177541       add(b(u-j, o+j-1, [1, 3, 4, 1, 3, 3][t]), j=1..u)+
%p A177541       add(b(u+j-1, o-j, [2, 2, 2, 5, 6, 7][t]), j=1..o)))
%p A177541     end:
%p A177541 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177541 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 20 2013
%t A177541 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177541      Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 3, 3}[[t]]], {j, 1, u}] +
%t A177541      Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 6, 7}[[t]]], {j, 1, o}]]];
%t A177541 a[n_] := b[n, 0, 1];
%t A177541 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177541 Columns k=39,57 of A242784.
%K A177541 nonn
%O A177541 0,3
%A A177541 _R. H. Hardin_, May 10 2010
%E A177541 a(17)-a(22) from _Alois P. Heinz_, Oct 20 2013