A288078 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 3.

17454580, 1171704435, 40121261136, 945068384880, 17326957790896, 264477214235234, 3505018618003600, 41491242915292306, 447708887118504600, 4470547991985864322, 41790549086980226368, 369061676845849000520, 3101645444966543203008, 24954084939131951164980, 193145505023621965434976, 1444143475412182351017494, 10467259286591304015806600

Offset: 9

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, this sequence, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, A288263 f=9, A288264 f=10.

Column 4 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, 4, 3];
Table[a[n], {n, 9, 26}] (* Jean-François Alcover, Oct 17 2018 *)

PARI

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288078_ser(N) = {
  my(y = A000108_ser(N+1));
  y*(y-1)^9*(5008230*y^8 + 164100330*y^7 + 620429875*y^6 - 742482075*y^5 - 1203385090*y^4 + 1546511666*y^3 - 224365292*y^2 - 189952744*y + 41589680)/(y-2)^26;
};
Vec(A288078_ser(17))