A052303 Number of asymmetric Greg trees.

1, 1, 0, 0, 0, 0, 1, 4, 12, 42, 137, 452, 1491, 4994, 16831, 57408, 197400, 685008, 2395310, 8437830, 29917709, 106724174, 382807427, 1380058180, 4998370015, 18181067670, 66393725289, 243347195594, 894959868983, 3301849331598, 12217869541117, 45335177297876

Offset

0,8

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

Alois P. Heinz, Table of n, a(n) for n = 0..1668

Index entries for sequences related to trees

Formula

G.f.: 1+B(x)-B(x)^2 where B(x) is g.f. of A052301.

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(g(i), 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] 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, Apr 28 2020, after Alois P. Heinz *)

Crossrefs

Cf. A005263, A005264, A048159, A048160, A052300-A052302.

Sequence in context: A300124 A343517 A308371 * A017942 A149344 A178078

Adjacent sequences: A052300 A052301 A052302 * A052304 A052305 A052306

Keyword

nonn

Author

Christian G. Bower, Nov 15 1999

Status

approved