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A177534 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, down.

%I A177534 #16 Apr 20 2022 10:31:42
%S A177534 1,1,2,6,24,120,720,5034,40224,361584,3611520,39679200,475580160,
%T A177534 6175139244,86348433264,1293675609960,20674025187840,351037594569600,
%U A177534 6311110770685440,119767524064039062,2392482308124881520,50181968955048369480,1102681392427432825920
%N A177534 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, down.
%H A177534 Alois P. Heinz, <a href="/A177534/b177534.txt">Table of n, a(n) for n = 0..200</a>
%F A177534 a(n) ~ c * d^n * n!, where d = 0.99880260814201465936657157017137377717606254472452619578417647021809..., c = 1.0072348951217738673562195411256011395302888145883911883919110478... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177534 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177534       add(b(u-j, o+j-1, `if`(t=1, 1, t+1)), j=1..u)+
%p A177534       add(b(u+j-1, o-j, 2), j=1..o)))
%p A177534     end:
%p A177534 a:= n-> b(n, 0, 1):
%p A177534 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177534 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177534      Sum[b[u - j, o + j - 1, If[t == 1, 1, t + 1]], {j, 1, u}] +
%t A177534      Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
%t A177534 a[n_] := b[n, 0, 1];
%t A177534 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 20 2022, after _Alois P. Heinz_ *)
%Y A177534 Columns k=32,62 of A242784.
%K A177534 nonn
%O A177534 0,3
%A A177534 _R. H. Hardin_, May 10 2010
%E A177534 a(18)-a(22) from _Alois P. Heinz_, Oct 21 2013