A006408 Number of nonseparable rooted toroidal maps with n + 3 edges and n + 1 vertices. (Formerly M3672)

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

2,1

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.

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

Prog

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

Crossrefs

Column 2 of A342989.

Sequence in context: A286359 A201740 A024212 * A112460 A296594 A290559

Adjacent sequences: A006405 A006406 A006407 * A006409 A006410 A006411

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Title improved by Sean A. Irvine, Apr 03 2017

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

Status

approved