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

Offset: 3

Author

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

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A036572.

Programs

Magma

[Floor((n^2+8*n-16)/4): n in [3..60]]; // Vincenzo Librandi, Oct 21 2013

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 *)

PARI

Vec(-x^3*(x^3-4*x^2+4)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Sep 06 2013

Formula

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

Extensions

More terms from Ralf Stephan, Oct 13 2003