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

7,2

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.

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Example

a(8) = 2:
:    o        o     :
:   /|\     / | \   :
:  o o o   o  o  o  :
:  | |    ( ) |     :
:  o o    o o o     :
:  |      |         :
:  o      o         :
:  |                :
:  o                :

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<v, 0, add(binomial(A(i, min(i-1, h)), j)
       *b(n-i*j, i-1, h, v-j), j=0..min(n/i, v))))
    end:
A:= proc(n, k) option remember;
      `if`(n<2, n, add(b(n-1$2, j$2), j=1..min(k, n-1)))
    end:
a:= n-> b(n-1$2, 3$2):
seq(a(n), n=7..45);

Crossrefs

Column k=3 of A245120.

Sequence in context: A360303 A077931 A115451 * A291728 A268649 A316983

Adjacent sequences: A245119 A245120 A245121 * A245123 A245124 A245125

Keyword

nonn

Author

Alois P. Heinz, Jul 12 2014

Status

approved