OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
EXAMPLE
a(4) = 4: 2314, 2341, 3214, 3241.
a(5) = 4: 23514, 32514, 34152, 43152.
a(6) = 4: 341625, 346152, 431625, 436152.
a(7) = 4: 3471625, 4371625, 4517263, 5417263.
a(8) = 8: 34716258, 43716258, 45182736, 45817263, 54182736, 54817263, 56283741, 65283741.
a(9) = 12: 348172596, 438172596, 451827369, 459182736, 541827369, 549182736, 561928374, 569283741, 651928374, 659283741, 672938514, 762938514.
MAPLE
b:= proc(u, o) option remember; `if`(u+o<3, (u+o)!,
`if`(o>2, b(sort([o-3, u+2])[]), 0)+
`if`(u>2, b(sort([u-3, o+2])[]), 0))
end:
a:= n-> `if`(n=0, 1, add(b(sort([j-1, n-j])[]), j=1..n)):
seq(a(n), n=0..40);
MATHEMATICA
b[u_, o_] := b[u, o] = If[u + o < 3, (u + o)!,
If[o > 2, b @@ Sort[{o - 3, u + 2}], 0] +
If[u > 2, b @@ Sort[{u - 3, o + 2}], 0]];
a[n_] := If[n == 0, 1, Sum[b @@ Sort[{j - 1, n - j}], {j, 1, n}]];
a /@ Range[0, 40] (* Jean-François Alcover, Mar 15 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 03 2013
STATUS
approved