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

3,1

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