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Search: id:A003080
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| A003080 |
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Number of rooted triangular cacti with 2n+1 nodes (n triangles).
(Formerly M1448)
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+0
4
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| 1, 1, 2, 5, 13, 37, 111, 345, 1105, 3624, 12099, 41000, 140647, 487440, 1704115, 6002600, 21282235, 75890812, 272000538, 979310627, 3540297130, 12845634348, 46764904745, 170767429511, 625314778963, 2295635155206, 8447553316546
(list; graph; listen)
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OFFSET
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0,3
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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).
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 73, (3.4.20).
P. Leroux and B. Miloudi, ``G\'{e}n\'{e}ralisations de la formule d'Otter,'' Ann. Sci. Math. Qu\'{e}bec, Vol. 16, No. 1, pp. 53-80, 1992.
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 305, (4.2.34).
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LINKS
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Index entries for sequences related to cacti
N. J. A. Sloane, Transforms
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FORMULA
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a(n)=b(2n+1). b shifts left under transform T where Tb = EULER(E_2(b)). E_2(b) has g.f. (B(x^2)+B(x)^2)/2.
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CROSSREFS
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Cf. A003081, A034940, A034941.
Sequence in context: A126031 A151416 A114509 this_sequence A149854 A151442 A053732
Adjacent sequences: A003077 A003078 A003079 this_sequence A003081 A003082 A003083
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KEYWORD
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nonn,eigen,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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Sequence extended by Paul Zimmermann, Mar 15 1996. Additional comments from Christian G. Bower (bowerc(AT)usa.net).
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