A288274 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 4.

7034538511, 600398249550, 25766235457300, 750260619502310, 16789118602155860, 309197871098871838, 4892650539994184868, 68503375296263488977, 866831237081712285138, 10071757699155275906824, 108780460548715291414960, 1102776421660293787585728, 10575907938883627723298512, 96567859695821049858887188, 844021580327996006292420440

Offset: 11

Author

Gheorghe Coserea, Jun 08 2017

Keywords

• nonn

Links

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

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, this sequence, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.

Column 4 of A269924.

Cf. A000108.

Programs

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, 4, 4];
Table[a[n], {n, 11, 25}] (* Jean-François Alcover, Oct 16 2018 *)

Formula

G.f.: y*(y-1)^11*(1495900107*y^10 + 72057286944*y^9 + 525358145917*y^8 + 168001652997*y^7 - 2349735380723*y^6 + 817302422933*y^5 + 2199510551627*y^4 - 1660311974101*y^3 + 109057768182*y^2 + 147825658668*y - 23527494040)/(y-2)^32, where y=A000108(x).