A288272 a(n) is the number of rooted maps with n edges and 2 faces on an orientable surface of genus 4.

12317877, 792534015, 26225260226, 600398249550, 10743797911132, 160576594766588, 2089035241981688, 24325590127655531, 258634264294653390, 2548272396065512974, 23532893106071038404, 205518653220527665304, 1709552077642556424368, 13623964536133602210560, 104522878918062035228512

Offset

9,1

Links

Table of n, a(n) for n=9..23.

Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.

Formula

G.f.: y*(y-1)^9*(225225*y^8 + 25467156*y^7 + 207300366*y^6 + 77853486*y^5 - 660073489*y^4 + 222312257*y^3 + 269246651*y^2 - 140048085*y + 10034310)/(y-2)^26, where y=A000108(x).

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, 4];
Table[a[n], {n, 9, 23}] (* Jean-François Alcover, Oct 16 2018 *)

Crossrefs

Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, this sequence, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.

Column 2 of A269924.

Cf. A000108.

Sequence in context: A022217 A133373 A321987 * A247831 A161592 A164338

Adjacent sequences: A288269 A288270 A288271 * A288273 A288274 A288275

Keyword

nonn

Author

Gheorghe Coserea, Jun 08 2017

Status

approved