OFFSET
0,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..460
FORMULA
a(n) ~ c * d^n * n! * n, where d = 0.87361286073825385348141673848..., c = 0.2252746... . - Vaclav Kotesovec, Aug 28 2014
EXAMPLE
a(5) = 16: 13254, 14253, 14352, 15243, 15342, 23154, 24153, 24351, 25143, 25341, 34152, 34251, 35142, 35241, 45132, 45231.
a(6) = 192: 124365, 125364, 125463, ..., 635241, 645132, 645231.
a(7) = 1472: 1235476, 1236475, 1236574, ..., 7635241, 7645132, 7645231.
MAPLE
b:= proc(u, o, t) option remember; `if`(t=9, 0,
`if`(u+o=0, `if`(t>4, 1, 0),
add(b(u-j, o+j-1, [1, 3, 1, 5, 7, 9, 7, 5][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 2, 4, 2, 6, 8, 8, 8][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);
MATHEMATICA
b[u_, o_, t_] := b[u, o, t] = If[t == 9, 0,
If[u + o == 0, If[t > 4, 1, 0],
Sum[b[u - j, o + j - 1, {1, 3, 1, 5, 7, 9, 7, 5}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 2, 4, 2, 6, 8, 8, 8}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
a /@ Range[0, 25] (* after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 30 2013
STATUS
approved