A036572 Number of tetrahedra in largest triangulation of polygonal prism with regular polygonal base.

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

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. A036573.

Programs

Magma

[Ceiling((n*n+6*n-16)/4): n in [3..60]]; // Vincenzo Librandi, Oct 21 2013

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 *)

PARI

Vec(x^3*(2*x^2-3)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Sep 05 2013

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)

Extensions

More terms from Ralf Stephan, Oct 13 2003