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A245121 Number of n-node rooted identity trees with thinning limbs and root outdegree (branching factor) 2. 2
1, 1, 3, 4, 8, 12, 22, 36, 63, 107, 188, 327, 578, 1020, 1820, 3248, 5839, 10511, 19022, 34484, 62755, 114421, 209234, 383327, 703901, 1294822, 2386376, 4405083, 8144701, 15080416, 27961728, 51912054, 96496481, 179577543, 334558479, 623936240, 1164765120 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

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 = 4..1000

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 1.938950593419038561279875... and c = 0.929315638487153276953929... . - Vaclav Kotesovec, Jul 13 2014

EXAMPLE

a(7) = 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      :

: |     |     |              :

: 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, 2$2):

seq(a(n), n=4..45);

CROSSREFS

Column k=2 of A245120.

Sequence in context: A173534 A074331 A052952 * A153339 A275989 A033955

Adjacent sequences:  A245118 A245119 A245120 * A245122 A245123 A245124

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 12 2014

STATUS

approved

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Last modified April 18 12:42 EDT 2019. Contains 322209 sequences. (Running on oeis4.)