A006408 Number of nonseparable rooted toroidal maps with n + 3 edges and n + 1 vertices.

4, 39, 190, 651, 1792, 4242, 8988, 17490, 31812, 54769, 90090, 142597, 218400, 325108, 472056, 670548, 934116, 1278795, 1723414, 2289903, 3003616, 3893670, 4993300, 6340230, 7977060, 9951669, 12317634, 15134665, 18469056, 22394152, 26990832, 32348008, 38563140

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn

Comments

The number of faces is 2. - Andrew Howroyd, Apr 05 2021

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..1000
• T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus. III: Nonseparable maps, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

Crossrefs

Column 2 of A342989.

Programs

PARI

a(n) = {binomial(n+2,4)*(8*n^2 + 17*n - 6)/15} \\ Andrew Howroyd, Apr 05 2021

Formula

From Colin Barker, Apr 08 2013: (Start)

a(n) = (n*(12-28*n-45*n^2+20*n^3+33*n^4+8*n^5))/360.

G.f.: -x^2*(x^2 + 11*x + 4) / (x-1)^7. (End)

a(n) = binomial(n+2,4)*(8*n^2 + 17*n - 6)/15. - Andrew Howroyd, Apr 05 2021

Extensions

Title improved by Sean A. Irvine, Apr 03 2017

Terms a(11) and beyond from Andrew Howroyd, Apr 05 2021