login
A006408
Number of nonseparable rooted toroidal maps with n + 3 edges and n + 1 vertices.
(Formerly M3672)
2
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
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
KEYWORD
nonn
EXTENSIONS
Title improved by Sean A. Irvine, Apr 03 2017
Terms a(11) and beyond from Andrew Howroyd, Apr 05 2021
STATUS
approved