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Search: id:A014535
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| A014535 |
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B-trees of order 3 with n leaves. |
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10
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| 0, 1, 1, 1, 1, 2, 2, 3, 4, 5, 8, 14, 23, 32, 43, 63, 97, 149, 224, 332, 489, 727, 1116, 1776, 2897, 4782, 7895, 12909, 20752, 32670, 50426, 76767, 116206, 176289, 269615, 416774, 650647, 1023035, 1614864, 2551783, 4028217, 6344749, 9966479
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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A B-tree of order m is an ordered tree such that every node has at most m children, the root has at least 2 children, every node except for the root has 0 or at least m/2 children, all end-nodes are at the same level.
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LINKS
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F. Ruskey, Information on B-Trees
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to rooted trees
Ph. Flajolet and A. Odlyzko, Singularity analysis of generating functions, p. 20.
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 91
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FORMULA
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G.f. satisfies A(x) = x + A(x^2+x^3).
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MAPLE
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spec := [ B, {B=Union(Z, Subst(M, B)), M=Union(Prod(Z, Z), Prod(Z, Z, Z))} ]: seq(combstruct[count](spec, size=n), n=0..36); # from Paul.Zimmermann(AT)loria.fr
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CROSSREFS
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Sequence in context: A021993 A116676 A100483 this_sequence A123560 A060407 A074077
Adjacent sequences: A014532 A014533 A014534 this_sequence A014536 A014537 A014538
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KEYWORD
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nonn
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com)
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