A177543 - OEIS

%I #16 Apr 19 2022 06:28:32

%S 1,1,2,6,24,120,720,4768,35968,312064,3004160,31764480,365798400,

%T 4555499520,61232590848,882227765248,13547017240576,221038858829824,

%U 3818608204709888,69637156745773056,1336921845773107200,26947721453843251200,569023211226594803712

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

%H Alois P. Heinz, <a href="/A177543/b177543.txt">Table of n, a(n) for n = 0..175</a>

%F a(n) ~ c * d^n * n!, where d = 0.9598365530271216889440240044515..., c = 1.2474579024498809739499621681... . - _Vaclav Kotesovec_, Jan 17 2015

%p b:= proc(u, o, t) option remember; `if`(t>6, 0, `if`(u+o+t<7, (u+o)!,

%p       add(b(u-j, o+j-1, [1, 3, 1, 5, 1, 7][t]), j=1..u)+

%p       add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 2][t]), j=1..o)))

%p     end:

%p a:= n-> b(n, 0, 1):

%p seq(a(n), n=0..25);  # _Alois P. Heinz_, Oct 24 2013

%t b[u_, o_, t_] := b[u, o, t] = If[t > 6, 0, If[u + o + t < 7, (u + o)!,

%t      Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 1, 7}[[t]]], {j, 1, u}] +

%t      Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 2}[[t]]], {j, 1, o}]]];

%t a[n_] := b[n, 0, 1];

%t Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 19 2022, after _Alois P. Heinz_ *)

%Y Column k=42 of A242784.

%K nonn

%O 0,3

%A _R. H. Hardin_, May 10 2010

%E a(17)-a(22) from _Alois P. Heinz_, Oct 24 2013