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A134306
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Shapes of height-balanced AVL trees of height at most 6 with n nodes.
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3
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0, 1, 1, 2, 1, 4, 6, 4, 17, 32, 44, 60, 70, 184, 476, 872, 1553, 2720, 4288, 6312, 9004, 16088, 36900, 82984, 174374, 346048, 653096, 1199384, 2160732, 3812464, 6617304, 11307920, 18978577, 31327104, 50882720, 80963520, 125489856, 188637520, 273984664
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listen;
history;
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OFFSET
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0,4
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 239, Eq 79, A_5.
R. C. Richards, Shape distribution of height-balanced trees, Info. Proc. Lett., 17 (1983), 17-20.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..64
Wikipedia, AVL tree
Index entries for sequences related to rooted trees
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FORMULA
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a(n) = Sum_{h=0..6} A143897(h,n).
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MAPLE
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a:= proc(n) local B, z; B:= proc (x, y, d) if d>=1 then x+B(x^2+2*x*y, x, d-1) else x fi end; coeff(B(z, 0, 6), z, n) end: seq (a(n), n=0..64);
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CROSSREFS
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Cf. A006265, A036662.
Sequence in context: A217299 A217300 A036662 * A006265 A131452 A111104
Adjacent sequences: A134303 A134304 A134305 * A134307 A134308 A134309
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KEYWORD
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nonn,fini,full
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AUTHOR
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Alois P. Heinz, Aug 27 2008
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STATUS
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approved
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