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Search: id:A005419
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| A005419 |
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Number of ways of dissecting a polygon into n 7-gons.
(Formerly M3023)
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+0
4
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| 1, 1, 3, 16, 112, 1020, 10222, 109947, 1230840, 14218671, 168256840, 2031152928, 24931793768, 310420597116, 3912823963482, 49853370677834, 641218583442360, 8316918403772790, 108686334145327785
(list; graph; listen)
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OFFSET
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1,3
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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).
F. Harary, E. M. Palmer and R. C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.
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FORMULA
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See Mathematica code.
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MATHEMATICA
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p=7; 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
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Sequence in context: A141003 A002404 A097142 this_sequence A124537 A074523 A042437
Adjacent sequences: A005416 A005417 A005418 this_sequence A005420 A005421 A005422
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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 Robert A. Russell (russell(AT)post.harvard.edu), Dec 11 2004
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