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

11,1

Links

Table of n, a(n) for n=11..25.

Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

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 *)

Prog

(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))

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.

Sequence in context: A017352 A017472 A017604 * A274366 A224988 A327056

Adjacent sequences: A288077 A288078 A288079 * A288081 A288082 A288083

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved