A244703 Number of n-node unlabeled rooted trees with thinning limbs and root outdegree (branching factor) 2.

1, 1, 3, 4, 9, 13, 26, 42, 81, 138, 262, 467, 885, 1620, 3076, 5743, 10953, 20721, 39714, 75873, 146139, 281259, 544230, 1053552, 2047147, 3981790, 7766018, 15165195, 29676887, 58148087, 114129308, 224278526, 441368913, 869583189, 1715365690, 3387344619

Offset: 3

Author

Alois P. Heinz, Jul 04 2014

Keywords

• nonn

Comments

In a rooted tree with thinning limbs the outdegree of a parent node is larger than or equal to the outdegree of any of its child nodes.

Examples

			a(6) = 4:
    o        o      o        o
   / \      / \    / \      / \
  o   o    o   o  o   o    o   o
  |       / \     |   |   / \  |
  o      o   o    o   o  o   o o
  |      |        |
  o      o        o
  |
  o
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..1000

Crossrefs

Column k=2 of A244657.

Programs

Maple

b:= proc(n, i, h, v) option remember; `if`(n=0,
      `if`(v=0, 1, 0), `if`(i<1 or v<1 or n b(n-1$2, 2$2):
seq(a(n), n=3..50);

Mathematica

b[n_, i_, h_, v_] := b[n, i, h, v] = If[n == 0, If[v == 0, 1, 0], If[i < 1 || v < 1 || n < v, 0, If[n == v, 1, Sum[Binomial[A[i, Min[i - 1, h]] + j - 1, j]*b[n - i*j, i - 1, h, v - j], {j, 0, Min[n/i, v]}]]]];
A[n_, k_] := A[n, k] = If[n<2, n, Sum[b[n-1, n-1, j, j], {j, 1, Min[k, n-1] }]];
a[n_] := b[n-1, n-1, 2, 2];
a /@ Range[3, 50] (* Jean-François Alcover, Dec 27 2020, after Alois P. Heinz *)

Formula

a(n) ~ c * d^n / n^(3/2), where d = 2.0554620926822709065075792..., c = 1.0209036918758320315742... . - Vaclav Kotesovec, Aug 27 2014