A123869 Order of minimal triangulation of the orientable closed surface of genus n (S_n).

4, 7, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30, 30, 31, 31, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33, 33, 33

Offset

0,1

Comments

Number of vertices in a triangulation of the orientable closed surface S_n of genus n that has the smallest number of vertices.

References

J. L. Gross and J. Yellen, eds., Handbook of Graph Theory, CRC Press, 2004; p. 742, Fact F19.

M. Jungerman and G. Ringel, Minimal triangulations on orientable surfaces, Acta Math. 145 (1980), 121-154.

Ringel, Gerhard. Wie man die geschlossenen nichtorientierbaren Flächen in möglichst wenig Dreiecke zerlegen kann. (German) Math. Ann. 130 (1955), 317--326. MR0075591 (17,774b)

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = ceiling((7 + sqrt(1+48*n))/2), except a(2) = 10.

Mathematica

Join[{4, 7, 10}, Table[Ceiling[(7 +Sqrt[1+48*n])/2], {n, 3, 80}]] (* G. C. Greubel, Aug 08 2019 *)

Prog

(PARI) concat([4, 7, 10], vector(80, n, ceil((7 + sqrt(1+48*(n+2)))/2) )) \\ G. C. Greubel, Aug 08 2019
(Magma) [4, 7, 10] cat [Ceiling((7 + Sqrt(1+48*n))/2): n in [3..80]]; // G. C. Greubel, Aug 08 2019
(Sage) [4, 7, 10]+[ceil((7 + sqrt(1+48*n))/2) for n in (3..80)] # G. C. Greubel, Aug 08 2019

Crossrefs

See A250098 for number of triangles in a minimal triangulation.

Sequence in context: A118517 A282848 A093465 * A309688 A072125 A370759

Adjacent sequences: A123866 A123867 A123868 * A123870 A123871 A123872

Keyword

nonn

Author

N. J. A. Sloane, Nov 19 2006

Status

approved