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A000677
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Number of bicentered trees with n nodes.
(Formerly M2366 N0936)
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9
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0, 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108, 267, 619, 1541, 3762, 9497, 23907, 61216, 157211, 407919, 1063398, 2792026, 7365532, 19535887, 52037837, 139213244, 373820978, 1007420841, 2723783122, 7387129661, 20091790330, 54793762295, 149808274055, 410553630946
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,7
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COMMENTS
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See A000676 for more information.
On the bottom of first page 266 of article Cayley (1881) is a table of A000676 and A000677 for n = 1..13. - Michael Somos, Aug 20 2018
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REFERENCES
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N. L. Biggs et al., Graph Theory 1736-1936, Oxford, 1976, p. 49.
A. Cayley, On the analytical forms called trees, with application to the theory of chemical combinations, Reports British Assoc. Advance. Sci. 45 (1875), 257-305 = Math. Papers, Vol. 9, 427-460 (see p. 438).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Geoffrey Critzer, Table of n, a(n) for n = 0..200 (replacing the first version from N. J. A. Sloane)
Jean-François Alcover, Mathematica program
A. Cayley, On the analytical forms called trees, Amer. J. Math., 4 (1881), 266-268.
E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees)., J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.
J. Riordan, The enumeration of trees by height and diameter, IBM Journal 4 (1960), 473-478. (Annotated scanned copy)
N. J. A. Sloane, Maple program
Eric Weisstein's World of Mathematics, Bicentered Tree.
Index entries for sequences related to trees
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FORMULA
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a(n) = A000055(n) - A000676(n).
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EXAMPLE
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G.f. = x^2 + x^4 + x^5 + 3*x^6 + 4*x^7 + 11*x^8 + 20*x^9 + 51*x^10 + ... - Michael Somos, Aug 20 2018
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MAPLE
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See link for Maple program.
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MATHEMATICA
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See link.
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CROSSREFS
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Cf. A000055, A000676.
Sequence in context: A295962 A097072 A049977 * A110865 A152982 A001642
Adjacent sequences: A000674 A000675 A000676 * A000678 A000679 A000680
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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