A287046 a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 1.

12012, 649950, 17970784, 344468530, 5188948072, 65723863196, 729734918432, 7302676928666, 67173739068760, 576218752277476, 4660202610532480, 35839052357422132, 263868150558327376, 1870153808268516280, 12816868756802256832, 85256107136168684650, 552171259884681058744

Offset: 7

Author

Gheorghe Coserea, Jun 04 2017

Keywords

• nonn

Links

• Sean R. Carrell and Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
• Sean R. Carrell and Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, Journal of Combinatorial Theory, Series A, 133 (2015), 58-75.

Crossrefs

Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, A006295 f=2, A006296 f=3, A288071 f=4, A288072 f=5, this sequence, A287047 f=7, A287048 f=8, A288073 f=9, A288074 f=10.

Column 6 of A269921, column 1 of A270410.

Cf. A000108.

Programs

Mathematica

Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;
Q[n_, f_, g_] := Q[n, f, g] = 6/(n + 1) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 Q[n - 2, f, g - 1] + 1/2 Sum[l = n - k; Sum[v = f - u; Sum[j = g - i; Boole[l >= 1 && v >= 1 && j >= 0] (2 k - 1) (2 l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 6, 1];
Table[a[n], {n, 7, 23}] (* Jean-François Alcover, Oct 17 2018 *)

PARI

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A287046_ser(N) = {
  my(y = A000108_ser(N+1));
  2*y*(y-1)^7*(28457*y^6 + 179171*y^5 - 222214*y^4 - 172512*y^3 + 257232*y^2 - 59904*y - 4224)/(y-2)^20;
};
Vec(A287046_ser(17))