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

8,1

Links

Table of n, a(n) for n=8..24.

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, 3, 3];
Table[a[n], {n, 8, 25}] (* 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);
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))

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.

Sequence in context: A233664 A322690 A322680 * A112043 A114677 A172591

Adjacent sequences: A288074 A288075 A288076 * A288078 A288079 A288080

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved