A288077 a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 3.

1169740, 66449432, 1955808460, 40121261136, 647739636160, 8789123742880, 104395235785256, 1115525500250760, 10933959720960760, 99727841192820016, 855779329367736840, 6968569097113244096, 54217755730994858080, 405300088876353160320, 2924455840981270327952, 20446207814548586119000, 138958722742591452843432

Offset: 8

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, this sequence, A288078 f=4, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, A288263 f=9, A288264 f=10.

Column 3 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, 3, 3];
Table[a[n], {n, 8, 25}] (* Jean-François Alcover, Oct 17 2018 *)

PARI

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288077_ser(N) = {
  my(y = A000108_ser(N+1));
  -4*y*(y-1)^8*(28314*y^7 + 1229985*y^6 + 4821650*y^5 - 4914053*y^4 - 6967314*y^3 + 7429165*y^2 - 1071576*y - 263736)/(y-2)^23;
};
Vec(A288077_ser(17))