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A014535
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B-trees of order 3 with n leaves.
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9
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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; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| 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
| 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
| G.f. satisfies A(x) = x + A(x^2+x^3).
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MAPLE
| 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
| Sequence in context: A100483 A182613 A184259 * A205006 A123560 A060407
Adjacent sequences: A014532 A014533 A014534 * A014536 A014537 A014538
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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