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

9,1

Links

Table of n, a(n) for n=9..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, 4, 3];
Table[a[n], {n, 9, 26}] (* 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);
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))

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.

Sequence in context: A254000 A129478 A326137 * A183269 A032749 A235848

Adjacent sequences: A288075 A288076 A288077 * A288079 A288080 A288081

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved