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

11,1

Links

Table of n, a(n) for n=11..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)^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).

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 *)

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.

Sequence in context: A113640 A233623 A199633 * A078512 A235390 A082255

Adjacent sequences: A288271 A288272 A288273 * A288275 A288276 A288277

Keyword

nonn

Author

Gheorghe Coserea, Jun 08 2017

Status

approved