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A005701
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Number of exterior points formed by extending diagonals of n-gon in general position.
(Formerly M2968)
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5
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3, 14, 40, 90, 175, 308, 504, 780, 1155, 1650, 2288, 3094, 4095, 5320, 6800, 8568, 10659, 13110, 15960, 19250, 23023, 27324, 32200, 37700, 43875, 50778, 58464, 66990, 76415, 86800, 98208, 110704, 124355
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OFFSET
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0,1
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COMMENTS
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See Gouyou-Beauchamps for an interpretation in terms of closed paths in the first quadrant of the square grid.
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 74, Problem 8.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = (n+1)*(n+2)*(n+3)*(n+6)/12.
G.f.: (x-3)/(x-1)^5 [Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
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MATHEMATICA
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CoefficientList[Series[(x - 3) / (x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 09 2013 *)
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PROG
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(Magma) [(n+1)*(n+2)*(n+3)*(n+6)/12: n in [0..50]]; // Vincenzo Librandi, Jun 09 2013
(PARI) a(n) = (n+1)*(n+2)*(n+3)*(n+6)/12; \\ Michel Marcus, Dec 16 2017
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CROSSREFS
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A diagonal of the triangle in A179898.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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