A036573 Size of maximal triangulation of an n-antiprism with regular polygonal base.

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, 862, 892, 922, 953

Offset

3,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

Jesús A. De Loera, Francisco Santos, and Fumihiko Takeuchi, Extremal properties of optimal dissections of convex polytopes, SIAM Journal Discrete Mathematics, 14, 2001, 143-161.

Mike Develin, Maximal triangulations of a regular prism, arXiv:math/0309220 [math.CO], 2003.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

a(n) = floor((n^2 + 8*n - 16)/4). - Ralf Stephan, Oct 13 2003

From Colin Barker, Sep 06 2013: (Start)

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)). (End)

E.g.f.: (16 + 8*x - 2*x^2 - (16 - 9*x - x^2)*cosh(x) - (17 - 9*x - x^2)*sinh(x))/4. - Stefano Spezia, Dec 18 2025

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A036572.

Sequence in context: A311539 A311540 A311541 * A311542 A311543 A311544

Adjacent sequences: A036570 A036571 A036572 * A036574 A036575 A036576

Keyword

nonn,easy

Author

Jesus De Loera (deloera(AT)math.ucdavis.edu)

Extensions

More terms from Ralf Stephan, Oct 13 2003

Status

approved