A006424 Number of rooted toroidal maps with 4 faces and n vertices and without separating cycles or isthmuses. (Formerly M5104)

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

1,1

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)*(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

Prog

(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

Crossrefs

Column 4 of A343090.

Sequence in context: A250550 A292417 A117798 * A291112 A362168 A192370

Adjacent sequences: A006421 A006422 A006423 * A006425 A006426 A006427

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

Status

approved