A288086 a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 2.

4390386, 313530000, 11270290416, 276221817810, 5235847653036, 82234427131416, 1117259292848016, 13518984452463630, 148755268498286436, 1511718920778951024, 14358354462488121408, 128656798319026864068, 1095747149735034238680, 8924653047010981590288, 69866689045523025725664

Offset

9,1

Links

Table of n, a(n) for n=9..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, 6, 2];
Table[a[n], {n, 9, 23}] (* Jean-François Alcover, Oct 18 2018 *)

Prog

(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288086_ser(N) = {
  my(y = A000108_ser(N+1));
  6*y*(y-1)^9*(2211997*y^8 + 32071458*y^7 + 27414609*y^6 - 154896511*y^5 + 58087530*y^4 + 94331624*y^3 - 68497296*y^2 + 8775424*y + 1232896)/(y-2)^26;
};
Vec(A288086_ser(15))

Crossrefs

Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, A288083 f=3, A288084 f=4, A288085 f=5, this sequence, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10.

Column 6 of A269922, column 2 of A270410.

Cf. A000108.

Sequence in context: A254305 A237537 A276323 * A210297 A019288 A237910

Adjacent sequences: A288083 A288084 A288085 * A288087 A288088 A288089

Keyword

nonn

Author

Gheorghe Coserea, Jun 05 2017

Status

approved