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A177535 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, up.

%I A177535 #17 Apr 19 2022 11:33:19
%S A177535 1,1,2,6,24,120,720,5011,39856,356616,3545280,38768400,462487631,
%T A177535 5977005477,83186290826,1240460869290,19730730733920,333451122953921,
%U A177535 5966845400766578,112703780178989573,2240828272067529040,46780834679854338540,1023129822229674425971
%N A177535 Number of permutations of {1,...,n} avoiding adjacent step pattern up, down, down, down, down, up.
%H A177535 Alois P. Heinz, <a href="/A177535/b177535.txt">Table of n, a(n) for n = 0..200</a>
%F A177535 a(n) ~ c * d^n * n!, where d = 0.9941229421721758523485136789468386588070503717223814960732680334748287519..., c = 1.036291721564809563490641628457988175489113294377683691938047314400726... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177535 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177535       add(b(u-j, o+j-1, [1, 3, 4, 5, 6, 1][t]), j=1..u)+
%p A177535       add(b(u+j-1, o-j, [2, 2, 2, 2, 2, 7][t]), j=1..o)))
%p A177535     end:
%p A177535 a:= n-> b(n, 0, 1):
%p A177535 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 22 2013
%t A177535 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177535      Sum[b[u - j, o + j - 1, {1, 3, 4, 5, 6, 1}[[t]]], {j, 1, u}] +
%t A177535      Sum[b[u + j - 1, o - j, {2, 2, 2, 2, 2, 7}[[t]]], {j, 1, o}]]];
%t A177535 a[n_] := b[n, 0, 1];
%t A177535 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177535 Column k=33 of A242784.
%K A177535 nonn
%O A177535 0,3
%A A177535 _R. H. Hardin_, May 10 2010
%E A177535 a(17)-a(22) from _Alois P. Heinz_, Oct 22 2013