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A000676
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Number of centered trees with n nodes.
(Formerly M0831 N0316)
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6
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1, 1, 0, 1, 1, 2, 3, 7, 12, 27, 55, 127, 284, 682, 1618, 3979, 9823, 24722, 62651, 160744, 415146, 1081107, 2831730, 7462542, 19764010, 52599053, 140580206, 377244482, 1016022191, 2745783463, 7443742141, 20239038700, 55178647926
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| A tree has either a center or a bicenter and either a centroid or a bicentroid. (These terms were introduced by Jordan.)
If the number of edges in a longest path in the tree is 2m, then the middle node in the path is the unique center, otherwise the two middle nodes in the path are the unique bicenters.
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REFERENCES
| 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).
A. Cayley, On the analytical forms called trees, Amer. J. Math., 4 (1881), 266-268.
F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1994; pp. 35, 36.
C. Jordan, Sur les assemblages des lignes, J. Reine angew. Math., 70 (1869), 185-190.
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
| N. J. A. Sloane, Table of n, a(n) for n = 0..200
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. [This articles states incorrectly that A000676 and A000677 give the numbers of trees with respectively a centroid and bicentroid.]
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to trees
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CROSSREFS
| Cf. A102911 (trees with a bicentroid), A027416 (trees with a centroid), A000677 (trees with a bicenter), A000055 (trees), A000081 (rooted trees).
A000676+A000677 = A000055.
Sequence in context: A054272 A129016 A099163 * A182692 A032173 A130616
Adjacent sequences: A000673 A000674 A000675 * A000677 A000678 A000679
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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