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Search: id:A003444
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| A003444 |
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Number of dissections of a polygon.
(Formerly M3455)
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+0
6
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| 1, 4, 12, 43, 143, 504, 1768, 6310, 22610, 81752, 297160, 1086601, 3991995, 14732720, 54587280, 202997670, 757398510, 2834510744, 10637507400, 40023636310, 150946230006, 570534578704, 2160865067312, 8199711378716
(list; graph; listen)
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OFFSET
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4,2
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COMMENT
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Also number of necklaces of 2 colors with 2n beads and n-2 black ones. - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 03 2002
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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).
P. Lisonek, Closed forms for the number of polygon dissections. Journal of Symbolic Computation 20 (1995), 595-601.
R. C. Read, On general dissections of a polygon, Aequat. Math. 18 (1978), 370-388.
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FORMULA
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(1/(2n)) Sum_{d |(2n, k)} phi(d)*binomial(2n/d, k/d) with k=n-2 - Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 03 2002
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MATHEMATICA
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Table[(Plus@@(EulerPhi[ # ]Binomial[2n/#, (n-2)/# ] &)/@Intersection[Divisors[2n], Divisors[n-2]])/(2n), {n, 3, 32}]
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CROSSREFS
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Cf. A047996, A073020.
Sequence in context: A149352 A149353 A149354 this_sequence A149355 A149356 A149357
Adjacent sequences: A003441 A003442 A003443 this_sequence A003445 A003446 A003447
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KEYWORD
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nonn
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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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More terms from Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 03 2002
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