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A036573
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Size of maximal triangulation of an n-antiprism with regular polygonal base.
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2
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4, 8, 12, 17, 22, 28, 34, 41, 48, 56, 64, 73, 82, 92, 102, 113, 124, 136, 148, 161, 174, 188, 202, 217, 232, 248, 264, 281, 298, 316, 334, 353, 372, 392, 412, 433, 454, 476, 498, 521, 544, 568, 592, 617, 642, 668, 694, 721, 748, 776, 804, 833
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OFFSET
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3,1
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REFERENCES
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J. A. De Loera, F. Santos and F. Takeuchi, ``Extremal properties of optimal dissections of convex polytopes'', SIAM Journal Discrete Mathematics, 14, 2001, 143-161.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 3..1000
M. Develin, Maximal triangulations of a regular prism
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
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FORMULA
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a(n) = floor((n^2 + 8n - 16)/4). - Ralf Stephan, Oct 13 2003
a(n) = (-33+(-1)^n+16*n+2*n^2)/8. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: -x^3*(x^3-4*x^2+4) / ((x-1)^3*(x+1)). - Colin Barker, Sep 06 2013
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MATHEMATICA
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CoefficientList[Series[-(x^3 - 4 x^2 + 4)/((x - 1)^3 (x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 21 2013 *)
LinearRecurrence[{2, 0, -2, 1}, {4, 8, 12, 17}, 60] (* Harvey P. Dale, Nov 28 2014 *)
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PROG
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(PARI) Vec(-x^3*(x^3-4*x^2+4)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Sep 06 2013
(MAGMA) [Floor((n^2+8*n-16)/4): n in [3..60]]; // Vincenzo Librandi, Oct 21 2013
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CROSSREFS
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Cf. A036572.
Sequence in context: A311539 A311540 A311541 * A311542 A311543 A311544
Adjacent sequences: A036570 A036571 A036572 * A036574 A036575 A036576
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KEYWORD
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nonn,easy
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AUTHOR
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Jesus De Loera (deloera(AT)math.ucdavis.edu)
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EXTENSIONS
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More terms from Ralf Stephan, Oct 13 2003
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STATUS
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approved
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