A288264 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 3.

10369994005800, 1461629029629340, 99727841192820016, 4470547991985864322, 149789855223187292608, 4031165546220945277040, 91230456810047671200128, 1792206112041706943912462, 31276917257222840819283888, 493477269339182312960416344, 7136207296287499744197970400, 95626920613336304647976494116

Offset

15,1

Links

Table of n, a(n) for n=15..26.

Gheorghe Coserea, The g.f. as a rational function of y=A000108(x)

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, 10, 3];
Table[a[n], {n, 15, 26}] (* Jean-François Alcover, Oct 17 2018 *)

Crossrefs

Rooted maps of genus 3 with n edges and f faces for 1<=f<=10: A288075 f=1, A288076 f=2, A288077 f=3, A288078 f=4, A288079 f=5, A288080 f=6, A288081 f=7, A288262 f=8, A288263 f=9, this sequence.

Column 10 of A269923.

Cf. A000108.

Sequence in context: A112432 A230100 A122966 * A127225 A257141 A250492

Adjacent sequences: A288261 A288262 A288263 * A288265 A288266 A288267

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved