A052525 Number of unlabeled rooted trees with n leaves in which the degrees of the root and all internal nodes are >= 3.

0, 0, 0, 1, 1, 2, 3, 6, 10, 20, 36, 71, 136, 270, 531, 1070, 2147, 4367, 8895, 18262, 37588, 77795, 161444, 336383, 702732, 1472582, 3093151, 6513402, 13744384, 29063588, 61570853, 130669978, 277767990, 591373581, 1260855164

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Old name was "Non-planar unlabeled trees with neither unary nor binary nodes". I am leaving this alternative name here because it may help clarify the definitions of related sequences. - N. J. A. Sloane.

Examples

			For instance, with 7 leaves, the 6 choices are:
. [ *,*,*,*,*,*,* ]
. [ *,*,*,*,[ *,*,* ] ]
. [ *,*,*,[ *,*,*,* ] ]
. [ *,*,[ *,*,*,*,* ] ]
. [ *,*,[ *,*,[ *,*,* ] ] ]
. [ *,[ *,*,* ],[ *,*,* ] ]
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 95

Crossrefs

Cf. A052524 and A052526.

Programs

Maple

spec := [ S, {B=Union(S, Z), S=Set(B, 3 <= card)}, unlabeled ]: seq(combstruct[ count ](spec, size=n), n=0..50);

Formula

a(n) ~ c * d^n / n^(3/2), where d = 2.2318799173898687960533559522113115638..., c = 0.3390616344584879699709248904124... . - Vaclav Kotesovec, May 04 2015

Extensions

More terms from Paul Zimmermann, Oct 31 2002