A288273 a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 4.

351683046, 26225260226, 993494827480, 25766235457300, 517592962672296, 8615949311310872, 123981042854132536, 1587135819804394530, 18451302662846918700, 197822824662547694148, 1979281881126113225376, 18654346303702719912848, 166862901890503876520320, 1425340713681247480547040, 11686190470805703242554960

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.

Formula

G.f.: -2*y*(y-1)^10*(12317877*y^9 + 793781118*y^8 + 6094043038*y^7 + 2216299748*y^6 - 23375789497*y^5 + 7963356801*y^4 + 15368481377*y^3 - 10027219339*y^2 + 877859200*y + 252711200)/(y-2)^29, 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, 3, 4];
Table[a[n], {n, 10, 24}] (* 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, A288272 f=2, this sequence, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.

Column 3 of A269924.

Cf. A000108.

Sequence in context: A257384 A186628 A032757 * A219271 A167517 A227642

Adjacent sequences: A288270 A288271 A288272 * A288274 A288275 A288276

Keyword

nonn

Author

Gheorghe Coserea, Jun 08 2017

Status

approved