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A052525
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Number of unlabeled rooted trees with n leaves in which the degrees of the root and all internal nodes are >= 3.
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1
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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
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0,6
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..34.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 95
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EXAMPLE
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For instance, with 7 leaves, the 6 choices are:
. [ *,*,*,*,*,*,* ]
. [ *,*,*,*,[ *,*,* ] ]
. [ *,*,*,[ *,*,*,* ] ]
. [ *,*,[ *,*,*,*,* ] ]
. [ *,*,[ *,*,[ *,*,* ] ] ]
. [ *,[ *,*,* ],[ *,*,* ] ]
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MAPLE
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spec := [ S, {B=Union(S, Z), S=Set(B, 3 <= card)}, unlabeled ]: seq(combstruct[ count ](spec, size=n), n=0..50);
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CROSSREFS
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Cf. A052524 and A052526.
Sequence in context: A173125 A047131 A008927 * A006606 A120421 A005418
Adjacent sequences: A052522 A052523 A052524 * A052526 A052527 A052528
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from Paul.Zimmermann(AT)loria.fr, Oct 31 2002
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STATUS
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approved
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