A213920 Number of rooted trees with n nodes such that no more than two subtrees corresponding to children of any node have the same number of nodes.

0, 1, 1, 2, 3, 7, 15, 34, 79, 190, 457, 1132, 2823, 7126, 18136, 46541, 120103, 312109, 815012, 2137755, 5632399, 14895684, 39519502, 105198371, 280815067, 751490363, 2016142768, 5420945437, 14604580683, 39425557103, 106618273626, 288792927325, 783516425820

Offset: 0

Author

Alois P. Heinz, Mar 05 2013

Keywords

• nonn

Comments

Coincides with A248869 up to a(9) = 190.

a(n+1)/a(n) tends to 2.845331... - Vaclav Kotesovec, Jun 04 2019

Examples

			:  o  :  o  :    o   o  :    o     o   o  :
:     :  |  :   / \  |  :    |    / \  |  :
:     :  o  :  o   o o  :    o   o   o o  :
:     :     :        |  :   / \  |     |  :
:     :     :        o  :  o   o o     o  :
:     :     :           :              |  :
: n=1 : n=2 :  n=3      :  n=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 o     o :
:  / \  |             |                 | :
: o   o o             o                 o :
:                                       | :
: n=5                                   o :
:.........................................:
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2213

Crossrefs

Cf. A000081, A032305, A248869.

Column k=2 of A318753.

Programs

Maple

g:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      binomial(g((i-1)$2)+j-1, j)*g(n-i*j, i-1), j=0..min(2, n/i))))
    end:
a:= n-> g((n-1)$2):
seq(a(n), n=0..40);

Mathematica

g[n_, i_] := g[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[g[i-1, i-1]+j-1, j]*g[n-i*j, i-1], {j, 0, Min[2, n/i]}]]]; a[n_] := g[n-1, n-1]; Table[ a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 21 2017, translated from Maple *)