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A005040
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Number of dissections of a polygon.
(Formerly M1851)
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4
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1, 1, 2, 8, 33, 194, 1196, 8196, 58140, 427975, 3223610, 24780752, 193610550, 1534060440, 12302123640, 99699690472, 815521503060, 6725991120004, 55882668179880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.
E. V. Konstantinova, A survey of the cell-growth problem and some its variations, preprint, 2001.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| E. V. Konstantinova, Com2Mac - Preprints
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FORMULA
| See Mathematica code.
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MATHEMATICA
| p=5; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2)) + If[OddQ[n], If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/2, (n-1)/2]/((p-2)n+2)], 3Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+Plus @@ Map[EulerPhi[ # ]Binomial[((p-1)n+1)/#, (n-1)/# ]/((p-1)n+1)&, Complement[Divisors[GCD[p, n-1]], {1, 2}]])/2, {n, 1, 20}] - Robert A. Russell (russell(AT)post.harvard.edu), Dec 11 2004
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CROSSREFS
| Cf. A005419, A004127, A005036, A000207.
Sequence in context: A150888 A030977 A030821 * A191551 A172448 A026577
Adjacent sequences: A005037 A005038 A005039 * A005041 A005042 A005043
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KEYWORD
| nonn,more
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Oct 13 2001
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