A006424 Number of rooted toroidal maps with 4 faces and n vertices and without separating cycles or isthmuses.

20, 831, 12656, 109075, 648792, 2978245, 11293436, 36973989, 107727724, 285451894, 699013380, 1601397330, 3465135024, 7135903782, 14072047976, 26707904230, 48991682628, 87164772761, 150869282184, 254695011933, 420306632200, 679327313795, 1077197343300, 1678276223715

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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.

Crossrefs

Column 4 of A343090.

Programs

PARI

a(n) = {n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(136*n^7 + 6554*n^6 + 98165*n^5 + 516860*n^4 + 763064*n^3 + 306776*n^2 + 2220955*n - 586110)/19958400} \\ Andrew Howroyd, Apr 04 2021

Formula

a(n) = n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(136*n^7 + 6554*n^6 + 98165*n^5 + 516860*n^4 + 763064*n^3 + 306776*n^2 + 2220955*n - 586110)/19958400. - Andrew Howroyd, Apr 04 2021

Extensions

Name clarified and terms a(9) and beyond from Andrew Howroyd, Apr 04 2021