A288073 a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 1.

1385670, 126264820, 5593305476, 164767964504, 3682811916980, 67173739068760, 1046677747672360, 14373136466094880, 177882700353757460, 2017523504473479992, 21241931655650633720, 209732362862241103248, 1957830216739337392584, 17394726697224718134384, 147908195064869691109072

Offset

10,1

Links

Table of n, a(n) for n=10..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, 9, 1];
Table[a[n], {n, 10, 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);
A288073_ser(N) = {
  my(y = A000108_ser(N+1));
  -2*y*(y-1)^10*(58911256*y^9 + 315266323*y^8 - 563073084*y^7 - 706445836*y^6 + 1588166368*y^5 - 488205920*y^4 - 472512192*y^3 + 315108288*y^2 - 44342784*y - 2179584)/(y-2)^29;
};
Vec(A288073_ser(17))

Crossrefs

Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, A006295 f=2, A006296 f=3, A288071 f=4, A288072 f=5, A287046 f=6, A287047 f=7, A287048 f=8, this sequence, A288074 f=10.

Column 9 of A269921.

Sequence in context: A229420 A249882 A252446 * A237240 A052242 A234548

Adjacent sequences: A288070 A288071 A288072 * A288074 A288075 A288076

Keyword

nonn

Author

Gheorghe Coserea, Jun 05 2017

Status

approved