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A177531 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down.

%I A177531 #14 Apr 19 2022 11:32:52
%S A177531 1,1,2,6,24,120,710,4900,38640,342720,3376800,36603975,432850200,
%T A177531 5545086300,76500496800,1130799033000,17829310686875,298684478837750,
%U A177531 5298029559119250,99196696006173000,1955043380032965000,40458045505003152500,877115498011253207500
%N A177531 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, down, down.
%H A177531 Alois P. Heinz, <a href="/A177531/b177531.txt">Table of n, a(n) for n = 0..200</a>
%F A177531 a(n) ~ c * d^n * n!, where d = 0.9854377717049233842779147747459503689075051143455990422632259770134..., c = 1.077575450109847511736343360036618345267367515043056772740942767... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177531 b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o+t<6, (u+o)!,
%p A177531       add(b(u-j, o+j-1, [1, 1, 4, 5, 6][t]), j=1..u)+
%p A177531       add(b(u+j-1, o-j, [2, 3, 3, 2, 2][t]), j=1..o)))
%p A177531     end:
%p A177531 a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
%p A177531 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 21 2013
%t A177531 b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o + t < 6, (u + o)!,
%t A177531      Sum[b[u - j, o + j - 1, {1, 1, 4, 5, 6}[[t]]], {j, 1, u}] +
%t A177531      Sum[b[u + j - 1, o - j, {2, 3, 3, 2, 2}[[t]]], {j, 1, o}]]];
%t A177531 a[n_] := b[n, 0, 1];
%t A177531 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177531 Columns k=24,28 of A242784.
%K A177531 nonn
%O A177531 0,3
%A A177531 _R. H. Hardin_, May 10 2010
%E A177531 a(17)-a(22) from _Alois P. Heinz_, Oct 21 2013