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Search: id:A054362
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| A054362 |
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Number of unlabeled 4-gonal cacti having n polygons. |
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+0
1
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| 1, 1, 1, 3, 11, 52, 307, 1936, 13207, 93496, 683988, 5127163, 39230669, 305299420, 2410624122, 19273255184, 155780437711, 1271253542364, 10462650241996, 86765190816362, 724450039738076, 6086167189623746, 51416796881915019
(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).
Index entries for sequences related to cacti
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MAPLE
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with(combinat): with(numtheory): m := 4: for p from 2 to 28 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: A129097 A014510 A058799 this_sequence A129833 A107958 A053557
Adjacent sequences: A054359 A054360 A054361 this_sequence A054363 A054364 A054365
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (plouffe(AT)math.uqam.ca)
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EXTENSIONS
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More terms and Maple program from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2006
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