A288081 a(n) is the number of rooted maps with n edges and 7 faces on an orientable surface of genus 3.

20465052608, 2079913241120, 104395235785256, 3505018618003600, 89390908732820144, 1857975645023518752, 32904419378927915376, 511895831411154922176, 7151648337964982801760, 91230456810047671200128, 1076401288635137599528944, 11867194568934207062990560

Offset

12,1

Links

Table of n, a(n) for n=12..23.

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) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 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] (2 k - 1) (2 l - 1) Q[k - 1, u, i] Q[l - 1, v, j], {i, 0, g}], {u, 1, f}], {k, 1, n}]);
a[n_] := Q[n, 7, 3];
Table[a[n], {n, 12, 27}] (* 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);
A288081_ser(N) = {
  my(y = A000108_ser(N+1));
  -8*y*(y-1)^12*(14699198844*y^11 + 323418619692*y^10 + 1093150970776*y^9 - 2010290018547*y^8 - 3822380209098*y^7 + 7160304314725*y^6 - 371305853280*y^5 - 4606441266688*y^4 + 2480182576832*y^3 - 129107145168*y^2 - 150618243904*y + 20945187392)/(y-2)^35;
};
Vec(A288081_ser(12))

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, A288080 f=6, this sequence, A288262 f=8, A288263 f=9, A288264 f=10.

Column 7 of A269923.

Cf. A000108.

Sequence in context: A118466 A003810 A003803 * A172794 A068243 A034656

Adjacent sequences: A288078 A288079 A288080 * A288082 A288083 A288084

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved