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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

REFERENCES

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.

LINKS

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

M. Develin, Maximal triangulations of a regular prism

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

FORMULA

a(n) = ceil((n*n+6*n-16)/4) = A004116(n) - 3. - Ralf Stephan, Oct 13 2003

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)). - Colin Barker, Sep 05 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 *)

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 February 22 01:04 EST 2019. Contains 320381 sequences. (Running on oeis4.)