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Search: id:A006080
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| A006080 |
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Number of rooted projective plane trees with n nodes.
(Formerly M1188)
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+0
5
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| 1, 1, 2, 4, 9, 21, 56, 155, 469, 1480, 4882, 16545, 57384, 202060, 720526, 2593494, 9408469, 34350507, 126109784, 465200333, 1723346074, 6408356210, 23911272090, 89495909409, 335916761128, 1264114452996, 4768464309416
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Number of rooted planar trees that can be turned over.
Also bracelets (or necklaces) with n-1 black beads and n-1 white beads such that the beads switch colors when bracelet is turned over.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
P. K. Stockmeyer, The charm bracelet problem and its applications, pp. 339-349 of Graphs and Combinatorics (Washington, Jun 1973), Ed. by R. A. Bari and F. Harary. Lect. Notes Math., Vol. 406. Springer-Verlag, 1974.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
Index entries for sequences related to trees
Index entries for sequences related to rooted trees
Index entries for sequences related to bracelets
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FORMULA
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Stockmeyer gives g.f.
a(n) = A003239(n)/2 + 2^(n-3). (n>=2)
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CROSSREFS
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Cf. A006079, A006081, A006082.
Sequence in context: A001430 A148073 A057513 this_sequence A148074 A130866 A123458
Adjacent sequences: A006077 A006078 A006079 this_sequence A006081 A006082 A006083
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, formula and additional comments from Christian G. Bower (bowerc(AT)usa.net), Dec 13 2001
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