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A177551 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, up, up.

%I A177551 #16 Apr 19 2022 11:32:31
%S A177551 1,1,2,6,24,120,720,5006,39776,355536,3530880,38581456,459905790,
%T A177551 5938902464,82590382604,1230586598456,19557934834104,330265974019619,
%U A177551 5905113439990368,111448391640387360,2214092715361273978,46185648021443324656,1009303225985497077402
%N A177551 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, up, up.
%H A177551 Alois P. Heinz, <a href="/A177551/b177551.txt">Table of n, a(n) for n = 0..450</a>
%F A177551 a(n) ~ c * d^n * n!, where d = 0.993326320961568877764783962159580548643374705129260577..., c = 1.0404765828695886736964990440705643676428197038942922... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177551 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177551       add(b(u-j, o+j-1, [1, 1, 4, 1, 1, 4][t]), j=1..u)+
%p A177551       add(b(u+j-1, o-j, [2, 3, 3, 5, 6, 7][t]), j=1..o)))
%p A177551     end:
%p A177551 a:= n-> b(n, 0, 1):
%p A177551 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 23 2013
%t A177551 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177551      Sum[b[u - j, o + j - 1, {1, 1, 4, 1, 1, 4}[[t]]], {j, 1, u}] +
%t A177551      Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 6, 7}[[t]]], {j, 1, o}]]];
%t A177551 a[n_] := b[n, 0, 1];
%t A177551 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177551 Columns k=55,59 of A242784.
%K A177551 nonn
%O A177551 0,3
%A A177551 _R. H. Hardin_, May 10 2010