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A177538 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, down.

%I A177538 #15 Apr 19 2022 11:39:44
%S A177538 1,1,2,6,24,120,720,4941,38736,341496,3354939,36244098,427006404,
%T A177538 5448087216,74864913552,1102353646680,17314190063037,288936154260522,
%U A177538 5105249306345502,95216905474054011,1869347069817467076,38535066745735462848,832195054189721911392
%N A177538 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, up, down, down.
%H A177538 Alois P. Heinz, <a href="/A177538/b177538.txt">Table of n, a(n) for n = 0..200</a>
%F A177538 a(n) ~ c * d^n * n!, where d = 0.98162590771907099517875504406285427992737137228..., c = 1.1133866874983726502599853171771818959460675... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177538 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177538       add(b(u-j, o+j-1, [1, 3, 4, 1, 6, 7][t]), j=1..u)+
%p A177538       add(b(u+j-1, o-j, [2, 2, 2, 5, 2, 2][t]), j=1..o)))
%p A177538     end:
%p A177538 a:= n-> b(n, 0, 1):
%p A177538 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 22 2013
%t A177538 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177538      Sum[b[u - j, o + j - 1, {1, 3, 4, 1, 6, 7}[[t]]], {j, 1, u}] +
%t A177538      Sum[b[u + j - 1, o - j, {2, 2, 2, 5, 2, 2}[[t]]], {j, 1, o}]]];
%t A177538 a[n_] := b[n, 0, 1];
%t A177538 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177538 Columns k=36,54 of A242784.
%K A177538 nonn
%O A177538 0,3
%A A177538 _R. H. Hardin_, May 10 2010
%E A177538 a(17)-a(22) from _Alois P. Heinz_, Oct 22 2013