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 A052525 Number of unlabeled rooted trees with n leaves in which the degrees of the root and all internal nodes are >= 3. 2

%I

%S 0,0,0,1,1,2,3,6,10,20,36,71,136,270,531,1070,2147,4367,8895,18262,

%T 37588,77795,161444,336383,702732,1472582,3093151,6513402,13744384,

%U 29063588,61570853,130669978,277767990,591373581,1260855164

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

%C 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_.

%H Vaclav Kotesovec, <a href="/A052525/b052525.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=95">Encyclopedia of Combinatorial Structures 95</a>

%F a(n) ~ c * d^n / n^(3/2), where d = 2.2318799173898687960533559522113115638..., c = 0.3390616344584879699709248904124... . - _Vaclav Kotesovec_, May 04 2015

%e For instance, with 7 leaves, the 6 choices are:

%e . [ *,*,*,*,*,*,* ]

%e . [ *,*,*,*,[ *,*,* ] ]

%e . [ *,*,*,[ *,*,*,* ] ]

%e . [ *,*,[ *,*,*,*,* ] ]

%e . [ *,*,[ *,*,[ *,*,* ] ] ]

%e . [ *,[ *,*,* ],[ *,*,* ] ]

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

%Y Cf. A052524 and A052526.

%K easy,nonn

%O 0,6

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

%E More terms from _Paul Zimmermann_, Oct 31 2002

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Last modified January 27 09:05 EST 2023. Contains 359838 sequences. (Running on oeis4.)