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Search: id:A003081
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| A003081 |
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Number of triangular cacti with 2n+1 nodes (n triangles).
(Formerly M1152)
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+0
3
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| 1, 1, 1, 2, 4, 8, 19, 48, 126, 355, 1037, 3124, 9676, 30604, 98473, 321572, 1063146, 3552563, 11982142, 40746208, 139573646, 481232759, 1669024720, 5819537836, 20390462732, 71762924354, 253601229046, 899586777908, 3202234779826
(list; graph; listen)
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OFFSET
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0,4
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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. 306, (4.2.35).
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 73, (3.4.21).
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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Index entries for sequences related to cacti
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FORMULA
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a(n)=b(2n+1). A003080(n)=c(2n+1). G.f.: B(x)=C(x)+(C(x^3)-C(x)^3)/3.
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CROSSREFS
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Cf. A003080, A034940, A034941.
Sequence in context: A151526 A099526 A005703 this_sequence A100133 A099598 A128816
Adjacent sequences: A003078 A003079 A003080 this_sequence A003082 A003083 A003084
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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 (njas(AT)research.att.com).
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EXTENSIONS
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Extended with formula by Christian G. Bower (bowerc(AT)usa.net), 10/98.
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