OFFSET
5,6
LINKS
Alois P. Heinz, Table of n, a(n) for n = 5..900
EXAMPLE
a(9) = 1:
o
/ ( ) \
o o o o
/( )\
o o o o
MAPLE
b:= proc(n, i, t, k) option remember; `if`(n=0, `if`(t in [0, k],
1, 0), `if`(i<1 or t>n, 0, add(binomial(b((i-1)$2, k$2)+j-1, j)*
b(n-i*j, i-1, max(0, t-j), k), j=0..n/i)))
end:
a:= n-> b(n-1$2, 4$2) -b(n-1$2, 5$2):
seq(a(n), n=5..50);
MATHEMATICA
b[n_, i_, t_, k_] := b[n, i, t, k] = If[n == 0, If[t == 0 || t == k, 1, 0], If[i < 1, 0, Sum[Binomial[b[i - 1, i - 1, k, k] + j - 1, j]*b[n - i*j, i - 1, Max[0, t - j], k], {j, 0, n/i}]] // FullSimplify]; a[n_] := b[n - 1, n - 1, 4, 4] - b[n - 1, n - 1, 5, 5]; Table[a[n], {n, 5, 50}] (* Jean-François Alcover, Feb 06 2015, after Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 29 2014
STATUS
approved