OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..170
FORMULA
a(n) ~ c * d^n * n!, where d = 0.9928637443921790380857377558103269268777241137790934589694993..., c = 1.0369478195304845650491426260146999487076420703190374702807322... . - Vaclav Kotesovec, Aug 29 2014
MAPLE
b:= proc(u, o, t) option remember; `if`(t>5, 0, `if`(u+o=0, 1,
add(b(u-j, o+j-1, `if`(t=1, 1, t+1)), j=1..u)+
add(b(u+j-1, o-j, 2), j=1..o)))
end:
a:= n-> `if`(n=0, 1, add(b(j-1, n-j, 1), j=1..n)):
seq(a(n), n=0..25); # Alois P. Heinz, Oct 21 2013
MATHEMATICA
b[u_, o_, t_] := b[u, o, t] = If[t > 5, 0, If[u + o == 0, 1,
Sum[b[u - j, o + j - 1, If[t == 1, 1, t + 1]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, 2], {j, 1, o}]]];
a[n_] := If[n == 0, 1, Sum[b[j - 1, n - j, 1], {j, 1, n}]];
Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Apr 20 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 10 2010
EXTENSIONS
a(17)-a(22) from Alois P. Heinz, Oct 20 2013
STATUS
approved