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A177550 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, down, down.

%I A177550 #16 Apr 19 2022 07:25:18
%S A177550 1,1,2,6,24,120,720,4950,38880,343440,3369600,36352800,427680000,
%T A177550 5452027218,74846801304,1100895311340,17272089457920,287920937620800,
%U A177550 5081935953473280,94681381716805374,1856848184953043760,38236452673395920040,824863858830361247040
%N A177550 Number of permutations of {1,...,n} avoiding adjacent step pattern up, up, down, up, down, down.
%H A177550 Alois P. Heinz, <a href="/A177550/b177550.txt">Table of n, a(n) for n = 0..200</a>
%F A177550 a(n) ~ c * d^n * n!, where d = 0.98057763883233672986361278986560196505968263650602..., c = 1.129827226571293707156672292645277720979050046894688... . - _Vaclav Kotesovec_, Jan 17 2015
%p A177550 b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,
%p A177550       add(b(u-j, o+j-1, [1, 1, 4, 1, 6, 7][t]), j=1..u)+
%p A177550       add(b(u+j-1, o-j, [2, 3, 3, 5, 3, 2][t]), j=1..o)))
%p A177550     end:
%p A177550 a:= n-> b(n, 0, 1):
%p A177550 seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 29 2013
%t A177550 b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,
%t A177550      Sum[b[u - j, o + j - 1, {1, 1, 4, 1, 6, 7}[[t]]], {j, 1, u}] +
%t A177550      Sum[b[u + j - 1, o - j, {2, 3, 3, 5, 3, 2}[[t]]], {j, 1, o}]]];
%t A177550 a[n_] := b[n, 0, 1];
%t A177550 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)
%Y A177550 Column k=52 of A242784.
%K A177550 nonn
%O A177550 0,3
%A A177550 _R. H. Hardin_, May 10 2010
%E A177550 a(17)-a(22) from _Alois P. Heinz_, Oct 29 2013