

A052525


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


2



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
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OFFSET

0,6


COMMENTS

Old name was "Nonplanar 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.


LINKS

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


FORMULA

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


EXAMPLE

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


MAPLE

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


CROSSREFS

Cf. A052524 and A052526.
Sequence in context: A231331 A008927 A331488 * A006606 A120421 A005418
Adjacent sequences: A052522 A052523 A052524 * A052526 A052527 A052528


KEYWORD

easy,nonn


AUTHOR

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


EXTENSIONS

More terms from Paul Zimmermann, Oct 31 2002


STATUS

approved



