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Number of nonseparable rooted toroidal maps with n + 4 edges and n + 1 vertices.
(Formerly M4742)
2

%I M4742 #18 Apr 05 2021 21:36:45

%S 10,190,1568,8344,33580,111100,317680,811096,1891318,4094090,8328320,

%T 16071120,29636984,52540472,89974880,149432720,241497410,380839382,

%U 587453856,888181800,1318560100,1925051700,2767711440,3923348520,5489251950,7587551010,10370288640

%N Number of nonseparable rooted toroidal maps with n + 4 edges and n + 1 vertices.

%C The number of faces is 3. - _Andrew Howroyd_, Apr 05 2021

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Andrew Howroyd, <a href="/A006409/b006409.txt">Table of n, a(n) for n = 2..1000</a>

%H T. R. S. Walsh and A. B. Lehman, <a href="http://dx.doi.org/10.1016/0095-8956(75)90050-7">Counting rooted maps by genus. III: Nonseparable maps</a>, J. Combinatorial Theory Ser. B 18 (1975), 222-259.

%F a(n) = 10 * binomial(n + 4, 6) + 120 * binomial(n + 4, 7) + 328 * binomial(n + 4, 8) + 232 * binomial(n + 4, 9) [From Walsh]. - _Sean A. Irvine_, Apr 03 2017

%F a(n) = binomial(n + 4, 6)*(29*n^3 + 108*n^2 - 11*n - 12)/63. - _Andrew Howroyd_, Apr 05 2021

%o (PARI) a(n) = {binomial(n + 4, 6)*(29*n^3 + 108*n^2 - 11*n - 12)/63} \\ _Andrew Howroyd_, Apr 05 2021

%Y Column 3 of A342989.

%K nonn

%O 2,1

%A _N. J. A. Sloane_

%E Terms a(10) and beyond from _Andrew Howroyd_, Apr 05 2021