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 A036572 Number of tetrahedra in largest triangulation of polygonal prism with regular polygonal base. 2
 3, 6, 10, 14, 19, 24, 30, 36, 43, 50, 58, 66, 75, 84, 94, 104, 115, 126, 138, 150, 163, 176, 190, 204, 219, 234, 250, 266, 283, 300, 318, 336, 355, 374, 394, 414, 435, 456, 478, 500, 523, 546, 570, 594, 619, 644, 670, 696, 723, 750, 778, 806 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 LINKS Vincenzo Librandi, Table of n, a(n) for n = 3..1000 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. M. Develin, Maximal triangulations of a regular prism Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA a(n) = ceiling((n*n + 6*n - 16)/4) = A004116(n) - 3. - Ralf Stephan, Oct 13 2003 From Colin Barker, Sep 05 2013: (Start) a(n) = (-31 - (-1)^n + 12*n + 2*n^2)/8. a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). G.f.: x^3*(2*x^2-3) / ((x-1)^3*(x+1)). (End) MATHEMATICA CoefficientList[Series[(2 x^2 - 3)/((x - 1)^3 (x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 21 2013 *) LinearRecurrence[{2, 0, -2, 1}, {3, 6, 10, 14}, 60] (* Harvey P. Dale, Jun 05 2017 *) PROG (PARI) Vec(x^3*(2*x^2-3)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Sep 05 2013 (MAGMA) [Ceiling((n*n+6*n-16)/4): n in [3..60]]; // Vincenzo Librandi, Oct 21 2013 CROSSREFS Cf. A036573. Sequence in context: A259646 A310069 A310070 * A139328 A253620 A282731 Adjacent sequences:  A036569 A036570 A036571 * A036573 A036574 A036575 KEYWORD nonn,easy AUTHOR Jesus De Loera (deloera(AT)math.ucdavis.edu) EXTENSIONS More terms from Ralf Stephan, Oct 13 2003 STATUS approved

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Last modified September 28 03:06 EDT 2020. Contains 337392 sequences. (Running on oeis4.)