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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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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 305, (4.2.34).
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.
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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N. J. A. Sloane, Transforms
Index entries for sequences related to cacti
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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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