OFFSET
0,4
COMMENTS
A Greg tree can be described as a tree with 2-colored nodes where only the black nodes are counted and the white nodes are of degree at least 3.
LINKS
FORMULA
G.f.: 1 + B(x) - B(x)^2 where B(x) is g.f. of A052300.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(binomial(g(i)+j-1, j)*b(n-i*j, i-1), j=0..n/i)))
end:
g:= n-> `if`(n<1, 0, b(n-1$2)+b(n, n-1)):
a:= n-> `if`(n=0, 1, g(n)-add(g(j)*g(n-j), j=0..n)):
seq(a(n), n=0..40); # Alois P. Heinz, Jun 22 2018
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0,
Sum[Binomial[g[i] + j - 1, j]*b[n - i*j, i - 1], {j, 0, n/i}]]];
g[n_] := If[n < 1, 0, b[n - 1, n - 1] + b[n, n - 1]];
a[n_] := If[n == 0, 1, g[n] - Sum[g[j]*g[n - j], {j, 0, n}]];
a /@ Range[0, 40] (* Jean-François Alcover, Jun 11 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Nov 15 1999
STATUS
approved