A288263 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 3.

1384928666550, 176357530955320, 10933959720960760, 447708887118504600, 13767319160210071404, 341505418008822731328, 7151648337964982801760, 130468023103972196647776, 2121333601263313429701060, 31276917257222840819283888, 423834000658990977141751472, 5335660046838578422013157200

Offset: 14

Author

Gheorghe Coserea, Jun 07 2017

Keywords

• nonn

Links

• Gheorghe Coserea, The g.f. as a rational function of y=A000108(x)
• Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

Crossrefs

Rooted maps of genus 3 with n edges and f faces for 1<=f<=10: A288075 f=1, A288076 f=2, A288077 f=3, A288078 f=4, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, this sequence, A288264 f=10.

Column 9 of A269923.

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) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 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] (2k - 1) (2l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 9, 3];
Table[a[n], {n, 14, 25}] (* Jean-François Alcover, Oct 17 2018 *)