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A123869 Order of minimal triangulation of the orientable closed surface of genus n (S_n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..72.

FORMULA

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

CROSSREFS

See A250098 for number of triangles in a minimal triangulation.

Sequence in context: A118517 A282848 A093465 * A072125 A223024 A275340

Adjacent sequences:  A123866 A123867 A123868 * A123870 A123871 A123872

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 19 2006

STATUS

approved

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Last modified November 20 06:06 EST 2018. Contains 317385 sequences. (Running on oeis4.)