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Search: id:A054423
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| A054423 |
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Number of unlabeled 3-gonal cacti having n triangles. |
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+0
2
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| 1, 1, 1, 2, 7, 19, 86, 372, 1825, 9143, 47801, 254990, 1391302, 7713642, 43401974, 247216934, 1423531255, 8275108733, 48511773461, 286542497274, 1704002332513, 10195435737315, 61341136938138, 370933387552634
(list; graph; listen)
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OFFSET
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0,4
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LINKS
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Miklos Bona, Michel Bousquet, Gilbert Labelle, Pierre Leroux, Enumeration of m-ary cacti, Advances in Applied Mathematics, 24 (2000), 22-56 (pdf, dvi).
M. Bousquet and C. Lamathe, Enumeration of solid trees according to edge number and edge degree distribution, Discr. Math., 298 (2005), 115-141.
Index entries for sequences related to cacti
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MAPLE
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with(combinat): with(numtheory): m := 3: for p from 1 to 40 do s1 := 0: s2 := 0:
for d from 1 to p do if p mod d = 0 then s1 := s1+phi(p/d)*binomial(m*d, d) fi: od:
for d from 1 to p-1 do if gcd(m, p-1) mod d = 0 then s2 := s2+phi(d)*binomial((p*m)/d, (p-1)/d) fi: od:
printf(`%d, `, (s1+s2)/(m*p)-binomial(m*p, p)/(p*(m-1)+1)) od:
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CROSSREFS
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Sequence in context: A083309 A080873 A126162 this_sequence A137990 A056650 A045858
Adjacent sequences: A054420 A054421 A054422 this_sequence A054424 A054425 A054426
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com) Mar 15 2000
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EXTENSIONS
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More terms and Maple code from James A. Sellers (sellersj(AT)math.psu.edu), Mar 17 2000
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