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.
