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A177542 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down, down.

%I A177542 #14 Apr 19 2022 11:08:02
%S A177542 1,1,2,6,24,120,720,4976,39296,349056,3444480,37382400,442506240,
%T A177542 5674931536,78376004800,1159755383520,18305304913920,306984257241600,
%U A177542 5451042337781760,102170107109747648,2015786374006453760,41759419845040968960,906291283573022730240
%N A177542 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, up, down, down, down.
%H A177542 Alois P. Heinz, <a href="/A177542/b177542.txt">Table of n, a(n) for n = 0..175</a>
%F A177542 a(n) ~ c * d^n * n!, where d = 0.9864854125625269564394281614736489845203102136102401801..., c = 1.08769348749685060865572679319744616257509477068722272... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177542 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177542       add(b(u-j, o+j-1, [1, 3, 1, 5, 6, 7][t]), j=1..u)+
%p A177542       add(b(u+j-1, o-j, [2, 2, 4, 2, 4, 2][t]), j=1..o)))
%p A177542     end:
%p A177542 a:= n-> b(n, 0, 1):
%p A177542 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 24 2013
%t A177542 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177542      Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 6, 7}[[t]]], {j, 1, u}] +
%t A177542      Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 4, 2}[[t]]], {j, 1, o}]]];
%t A177542 a[n_] := b[n, 0, 1];
%t A177542 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177542 Columns k=40,58 of A242784.
%K A177542 nonn
%O A177542 0,3
%A A177542 _R. H. Hardin_, May 10 2010
%E A177542 a(17)-a(22) from _Alois P. Heinz_, Oct 24 2013