A052300 Number of rooted Greg trees.

1, 2, 6, 21, 78, 313, 1306, 5653, 25088, 113685, 523522, 2443590, 11533010, 54949539, 263933658, 1276652682, 6213207330, 30402727854, 149486487326, 738184395770, 3659440942282, 18205043615467, 90856842218506, 454770531433586, 2282393627458496, 11483114908752959

Offset

1,2

Comments

A rooted Greg tree can be described as a rooted tree with 2-colored nodes where only the black nodes are counted and the white nodes have at least 2 children.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences related to rooted trees

N. J. A. Sloane, Transforms

Formula

Satisfies a = EULER(a) + SHIFT_RIGHT(EULER(a)) - a.

a(n) ~ c * d^n / n^(3/2), where d = 5.33997181362574740496306748840603859910694551382103293340704... and c = 0.18146848896221859476228524468003196434835879494225205... - Vaclav Kotesovec, Jun 11 2021

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i)+j-1, j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> `if`(n<1, 0, b(n-1$2)+b(n, n-1)):
seq(a(n), n=1..40);  # Alois P. Heinz, Jun 22 2018

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i] + j - 1, j] b[n - i j, i - 1], {j, 0, n/i}]]];
a[n_] := If[n < 1, 0, b[n - 1, n - 1] + b[n, n - 1]];
a /@ Range[1, 40] (* Jean-François Alcover, Oct 02 2019, after Alois P. Heinz *)

Crossrefs

Cf. A005263, A005264, A048159, A048160, A052301-A052303.

Sequence in context: A287211 A357538 A150193 * A306832 A121941 A150194

Adjacent sequences: A052297 A052298 A052299 * A052301 A052302 A052303

Keyword

nonn,eigen

Author

Christian G. Bower, Nov 15 1999

Status

approved