A288079 a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 3.

211083730, 16476937840, 647739636160, 17326957790896, 357391270819604, 6087558311398000, 89390908732820144, 1165172136542282424, 13767319160210071404, 149789855223187292608, 1518921342035154605600, 14492634832409091816640, 131114130730951689447016, 1131791523345860091265696, 9370402052804684247760928

Offset: 10

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

Column 5 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, 5, 3];
Table[a[n], {n, 10, 27}] (* Jean-François Alcover, Oct 17 2018 *)

PARI

A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288079_ser(N) = {
  my(y = A000108_ser(N+1));
  -2*y*(y-1)^10*(83904012*y^9 + 2299548501*y^8 + 8375416306*y^7 - 11663434748*y^6 - 20521873396*y^5 + 30517603222*y^4 - 3781427784*y^3 - 7908127656*y^2 + 2862038656*y - 158105248)/(y-2)^29;
};
Vec(A288079_ser(15))