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Number of nonseparable rooted toroidal maps with n + 3 edges and n + 1 vertices.
(Formerly M3672)
2

%I M3672 #21 Apr 05 2021 21:36:31

%S 4,39,190,651,1792,4242,8988,17490,31812,54769,90090,142597,218400,

%T 325108,472056,670548,934116,1278795,1723414,2289903,3003616,3893670,

%U 4993300,6340230,7977060,9951669,12317634,15134665,18469056,22394152,26990832,32348008,38563140

%N Number of nonseparable rooted toroidal maps with n + 3 edges and n + 1 vertices.

%C The number of faces is 2. - _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="/A006408/b006408.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 From _Colin Barker_, Apr 08 2013: (Start)

%F a(n) = (n*(12-28*n-45*n^2+20*n^3+33*n^4+8*n^5))/360.

%F G.f.: -x^2*(x^2 + 11*x + 4) / (x-1)^7. (End)

%F a(n) = binomial(n+2,4)*(8*n^2 + 17*n - 6)/15. - _Andrew Howroyd_, Apr 05 2021

%o (PARI) a(n) = {binomial(n+2,4)*(8*n^2 + 17*n - 6)/15} \\ _Andrew Howroyd_, Apr 05 2021

%Y Column 2 of A342989.

%K nonn

%O 2,1

%A _N. J. A. Sloane_

%E Title improved by _Sean A. Irvine_, Apr 03 2017

%E Terms a(11) and beyond from _Andrew Howroyd_, Apr 05 2021