A288088 a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 2.

205633428, 19678611645, 925572602058, 29079129795702, 694146691745820, 13518984452463630, 224686278407291148, 3286157560248860532, 43241609165618454096, 520516978029736518606, 5805858136761540452700, 60619447491266688750132, 597358002436877437320936, 5593151345725345725640044

Offset

11,1

Links

Table of n, a(n) for n=11..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, 8, 2];
Table[a[n], {n, 11, 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);
A288088_ser(N) = {
  my(y = A000108_ser(N+1));
  3*y*(y-1)^11*(1455480376*y^10 + 18151410348*y^9 + 12284790745*y^8 - 111454641175*y^7 + 46880062914*y^6 + 129967691724*y^5 - 125047028168*y^4 + 14650142480*y^3 + 19075464224*y^2 - 6255822912*y + 360993920)/(y-2)^32;
};
Vec(A288088_ser(14))

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, A288086 f=6, A288087 f=7, this sequence, A288089 f=9, A288090 f=10.

Column 8 of A269922, column 2 of A270412.

Cf. A000108.

Sequence in context: A273094 A226079 A034641 * A233493 A187440 A092379

Adjacent sequences: A288085 A288086 A288087 * A288089 A288090 A288091

Keyword

nonn

Author

Gheorghe Coserea, Jun 05 2017

Status

approved