A135327 Number of genus-surfaces with n vertices.

1, 0, 1, 3, 21, 586, 50531, 16141671

Offset

3,4

Links

Table of n, a(n) for n=3..10.

Gennaro Amendola, Decomposition and Enumeration of Triangulated Surfaces, Experiment. Math. 17-2 (2008), 153-166; arXiv:0705.1835 [math.CO], 2007, table 2, page 20.

Example

a(3) = 1 because the unique surface with 3 vertices is on the closed surface S^2.
a(4) = 0 because there are no surface with 4 vertices in Amendola's table.
a(5) = 1 because the unique surface with 5 vertices is on the closed surface RP^2.
a(6) = 3 because there is a unique surface with 6 vertices on the closed surface T^2 and two on RP^2, so 1 + 2 = 3.
a(7) = 21 because there are 5 surfaces with 7 vertices on the closed surface T^2, 6 on RP^2 and 10 on K^2, so 5 + 6 + 10 = 21.
a(8) = 46 + 11 + 108 + 284 + 134 + 3 = 586 (see table).
a(9) = 230 + 1261 + 59 + 28 + 597 + 6919 + 18166 + 18199 + 4994 + 78 = 50531 (see table).
a(10) = 1513 + 50878 + 99177 + 3892 + 356 + 3864 + 82588 + 713714 + 3006044 + 5672821 + 4999850 + 1453490 + 53484 = 16141671.

Crossrefs

Cf. A108239.

Sequence in context: A135748 A145386 A344260 * A128679 A292331 A111432

Adjacent sequences: A135324 A135325 A135326 * A135328 A135329 A135330

Keyword

nonn,more

Author

Jonathan Vos Post, Dec 06 2007

Extensions

Edited by N. J. A. Sloane, Dec 07 2007

Missing a(5) = 1 inserted by Andrey Zabolotskiy, Nov 20 2017

Name corrected by Andrey Zabolotskiy, Sep 21 2021

Status

approved