A245122 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 3.

1, 2, 4, 9, 17, 35, 67, 131, 249, 484, 922, 1775, 3393, 6513, 12461, 23910, 45806, 87903, 168619, 323796, 621816, 1195123, 2297617, 4420093, 8506487, 16380013, 31554394, 60817066, 117266799, 226217218, 436572777, 842895506, 1628036630, 3145780899, 6080759314

Offset: 7

Author

Alois P. Heinz, Jul 12 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(8) = 2:
:    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 = 7..1000

Crossrefs

Column k=3 of A245120.

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, 3$2):
seq(a(n), n=7..45);