A006423 Number of rooted toroidal maps with 3 faces and n vertices and without separating cycles or isthmuses. (Formerly M4748)

10, 240, 2246, 12656, 52164, 173776, 495820, 1256992, 2902702, 6214208, 12494482, 23827440, 43430088, 76120288, 128926232, 211867328, 338940050, 529346384, 809006814, 1212404336, 1784810764, 2584951600, 3688170980, 5190163680, 7211346870, 9901950240, 13447909290

Offset

1,1

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 = 1..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

a(n) = n*(n + 1)*(n + 2)*(n + 3)*(29*n^5 + 762*n^4 + 5111*n^3 + 7902*n^2 + 8*n + 5088)/45360. - Andrew Howroyd, Apr 04 2021

Prog

(PARI) a(n) = {n*(n + 1)*(n + 2)*(n + 3)*(29*n^5 + 762*n^4 + 5111*n^3 + 7902*n^2 + 8*n + 5088)/45360}

Crossrefs

Column 3 of A343090.

Sequence in context: A177595 A013922 A215835 * A067423 A221099 A171204

Adjacent sequences: A006420 A006421 A006422 * A006424 A006425 A006426

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Name clarified and terms a(10) and beyond from Andrew Howroyd, Apr 04 2021

Status

approved