A288082 a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 2.

483, 15018, 258972, 3288327, 34374186, 313530000, 2583699888, 19678611645, 140725699686, 955708437684, 6216591472728, 38985279745230, 236923660397172, 1401097546161936, 8089830217844928, 45732525474843801, 253705943922820830, 1383896652090932364, 7434748752218650632, 39394773780853063650

Offset

5,1

Links

Table of n, a(n) for n=5..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) ((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, 2, 2];
Table[a[n], {n, 5, 24}] (* 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);
A288082_ser(N) = {
  my(y = A000108_ser(N+1));
  3*y*(y-1)^5*(7*y^4 + 294*y^3 + 309*y^2 - 547*y + 98)/(y-2)^14;
};
Vec(A288082_ser(20))

Crossrefs

Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, this sequence, A288083 f=3, A288084 f=4, A288085 f=5, A288086 f=6, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10.

Column 2 of A269922, column 2 of A270406.

Cf. A000108.

Sequence in context: A260976 A281047 A158330 * A251625 A156646 A177434

Adjacent sequences: A288079 A288080 A288081 * A288083 A288084 A288085

Keyword

nonn

Author

Gheorghe Coserea, Jun 05 2017

Status

approved