A288076 a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 3.

56628, 2668750, 66449432, 1171704435, 16476937840, 196924458720, 2079913241120, 19925913354061, 176357530955320, 1461629029629340, 11460411934448048, 85694099173907510, 614960028331370816, 4257157940494918160, 28549761695867223680, 186131532080726321441, 1183191417356212860200, 7351865732351585503652

Offset

7,1

Links

Table of n, a(n) for n=7..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) ((2n - 1)/3 Q[n - 1, f, g] + (2n - 1)/3 Q[n - 1, f - 1, g] + (2n - 3) (2n - 2) (2n - 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] (2k - 1) (2l - 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, 3];
Table[a[n], {n, 7, 24}] (* 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);
A288076_ser(N) = {
  my(y = A000108_ser(N+1));
  y*(y-1)^7*(1485*y^6 + 111969*y^5 + 453295*y^4 - 389693*y^3 - 443894*y^2 + 361702*y - 38236)/(y-2)^20;
};
Vec(A288076_ser(18))

Crossrefs

Rooted maps of genus 3 with n edges and f faces for 1<=f<=10: A288075 f=1, this sequence, A288077 f=3, A288078 f=4, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, A288263 f=9, A288264 f=10.

Column 2 of A269923.

Cf. A000108.

Sequence in context: A202433 A329270 A190836 * A031683 A202568 A145685

Adjacent sequences: A288073 A288074 A288075 * A288077 A288078 A288079

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved