A288278 a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 4.

182231849209410, 24325590127655531, 1587135819804394530, 68503375296263488977, 2221381417843144801098, 58089920897558352891672, 1281537868340178808063824, 24605894500188479477960928, 420612140517667008915254376, 6512251870890866709301451550, 92559480623350598649493386580

Offset

15,1

Links

Table of n, a(n) for n=15..25.

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)^15*(2141204115631518*y^14 + 62802256981978404*y^13 + 390904315702808387*y^12 - 17469926941849537*y^11 - 2715522908192830943*y^10 + 1209526054185992549*y^9 + 5862111891800632315*y^8 - 6084780630540788053*y^7 - 1344178041537337418*y^6 + 4359417524034703460*y^5 - 1779344954166712472*y^4 - 128701285301543888*y^3 + 220665627694548576*y^2 - 38233669153240512*y + 844773167217024)/(y-2)^44, 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, 8, 4];
Table[a[n], {n, 15, 25}] (* 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, A288273 f=3, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, this sequence, A288279 f=9, A288280 f=10.

Column 8 of A269924.

Cf. A000108.

Sequence in context: A245721 A320874 A348801 * A172566 A214947 A364413

Adjacent sequences: A288275 A288276 A288277 * A288279 A288280 A288281

Keyword

nonn

Author

Gheorghe Coserea, Jun 08 2017

Status

approved