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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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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: A017942 A135489 A100217 this_sequence A060897 A005190 A055542
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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njas
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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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