A288080 a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 3.

2198596400, 196924458720, 8789123742880, 264477214235234, 6087558311398000, 114899070275212424, 1857975645023518752, 26522236056202555206, 341505418008822731328, 4031165546220945277040, 44171448380277095027584, 453764845712090669861060, 4405234525240663358548000, 40682085269643556632419504, 359336179016097679450360000

Offset: 11

Author

Gheorghe Coserea, Jun 07 2017

Keywords

• nonn

Links

• 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, this sequence, A288081 f=7, A288262 f=8, A288263 f=9, A288264 f=10.

Column 6 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, 6, 3];
Table[a[n], {n, 11, 28}] (* Jean-François Alcover, Oct 17 2018 *)

PARI

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288080_ser(N) = {
  my(y = A000108_ser(N+1));
  2*y*(y-1)^11*(2360692395*y^10 + 57065162931*y^9 + 200199438395*y^8 - 321653197109*y^7 - 594662939878*y^6 + 999754510326*y^5 - 90653073868*y^4 - 435707439920*y^3 + 201952082336*y^2 - 14180151168*y - 3375786240)/(y-2)^32;
};
Vec(A288080_ser(15))