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A177548 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down, down.

%I A177548 #16 Apr 19 2022 07:29:00
%S A177548 1,1,2,6,24,120,720,5025,40080,359640,3585600,39322800,470448000,
%T A177548 6097392939,85106238492,1272746220570,20302567148160,344103461618400,
%U A177548 6175195781293440,116975122363277289,2332451810975205960,48833870901559002540,1071107370496773577440
%N A177548 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down, down.
%H A177548 Alois P. Heinz, <a href="/A177548/b177548.txt">Table of n, a(n) for n = 0..175</a>
%F A177548 a(n) ~ c * d^n * n!, where d = 0.99698626702423025316812958090212389097043667361318991688710688185165..., c = 1.018367520648807878150063272123153629935889863110044893080319840979... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177548 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177548       add(b(u-j, o+j-1, [1, 1, 4, 5, 6, 7][t]), j=1..u)+
%p A177548       add(b(u+j-1, o-j, [2, 3, 3, 2, 2, 2][t]), j=1..o)))
%p A177548     end:
%p A177548 a:= n-> b(n, 0, 1):
%p A177548 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 23 2013
%t A177548 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177548      Sum[b[u - j, o + j - 1, {1, 1, 4, 5, 6, 7}[[t]]], {j, 1, u}] +
%t A177548      Sum[b[u + j - 1, o - j, {2, 3, 3, 2, 2, 2}[[t]]], {j, 1, o}]]];
%t A177548 a[n_] := b[n, 0, 1];
%t A177548 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177548 Columns k=48,60 of A242784.
%K A177548 nonn
%O A177548 0,3
%A A177548 _R. H. Hardin_, May 10 2010
%E A177548 a(17)-a(22) from _Alois P. Heinz_, Oct 23 2013