A288076 a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 3.

56628, 2668750, 66449432, 1171704435, 16476937840, 196924458720, 2079913241120, 19925913354061, 176357530955320, 1461629029629340, 11460411934448048, 85694099173907510, 614960028331370816, 4257157940494918160, 28549761695867223680, 186131532080726321441, 1183191417356212860200, 7351865732351585503652

Offset: 7

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, this sequence, A288077 f=3, A288078 f=4, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, A288263 f=9, A288264 f=10.

Column 2 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, 2, 3];
Table[a[n], {n, 7, 24}] (* Jean-François Alcover, Oct 17 2018 *)

PARI

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288076_ser(N) = {
  my(y = A000108_ser(N+1));
  y*(y-1)^7*(1485*y^6 + 111969*y^5 + 453295*y^4 - 389693*y^3 - 443894*y^2 + 361702*y - 38236)/(y-2)^20;
};
Vec(A288076_ser(18))