A006410 Number of nonseparable rooted toroidal maps with n + 5 edges and n + 1 vertices. (Formerly M5102)

20, 651, 8344, 64667, 361884, 1607125, 5997992, 19535997, 57014776, 151986562, 375470160, 869285378, 1902886024, 3966657702, 7920130544, 15220758070, 28268206764, 50910912965, 89176474920, 152305796565, 254193384900, 415363487955, 665644575960, 1047743815755

Offset

2,1

Comments

The number of faces is 4. - 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

a(n) = 20 * binomial(n + 6, 8) + 471 * binomial(n + 6, 9) + 2734 * binomial(n + 6, 10) + 5388 * binomial(n + 6, 11) + 3264 * binomial(n + 6, 12) [From Walsh]. - Sean A. Irvine, Apr 03 2017

a(n) = binomial(n + 6, 8)*(136*n^4 + 790*n^3 + 447*n^2 - 180*n - 24)/495. - Andrew Howroyd, Apr 05 2021

Prog

(PARI) a(n) = {binomial(n + 6, 8)*(136*n^4 + 790*n^3 + 447*n^2 - 180*n - 24)/495} \\ Andrew Howroyd, Apr 05 2021

Crossrefs

Column 4 of A342989.

Sequence in context: A336412 A226731 A201724 * A159874 A203136 A034404

Adjacent sequences: A006407 A006408 A006409 * A006411 A006412 A006413

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms a(9) and beyond from Andrew Howroyd, Apr 05 2021

Status

approved