OFFSET
1,1
COMMENTS
A map on a torus has genus 1.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Colin Barker, 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.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
G.f.: x/(x-1)^7*(3*x^2-9*x-10). - Simon Plouffe, Master's thesis, Uqam 1992
From Colin Barker, Apr 22 2017: (Start)
a(n) = (n*(474 + 1247*n + 1215*n^2 + 545*n^3 + 111*n^4 + 8*n^5)) / 360.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
PROG
(PARI) Vec(x*(10 + 9*x - 3*x^2) / (1 - x)^7 + O(x^40)) \\ Colin Barker, Apr 22 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name improved by Sean A. Irvine, Apr 21 2017
STATUS
approved