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A006410 Number of nonseparable rooted toroidal maps with n + 5 edges and n + 1 vertices.
(Formerly M5102)
2
20, 651, 8344, 64667, 361884, 1607125, 5997992, 19535997, 57014776, 151986562, 375470160, 869285378, 1902886024, 3966657702, 7920130544, 15220758070, 28268206764, 50910912965, 89176474920, 152305796565, 254193384900, 415363487955, 665644575960, 1047743815755 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, Apr 05 2021
STATUS
approved

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Last modified July 21 11:45 EDT 2024. Contains 374472 sequences. (Running on oeis4.)