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

0,4

Comments

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

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

Links

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

Example

:  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 :
:.........................................:

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 *)

Crossrefs

Cf. A000081, A032305, A248869.

Column k=2 of A318753.

Sequence in context: A358734 A198683 A001932 * A248869 A005909 A003006

Adjacent sequences: A213917 A213918 A213919 * A213921 A213922 A213923

Keyword

nonn

Author

Alois P. Heinz, Mar 05 2013

Status

approved