A288084 a(n) is the number of rooted maps with n edges and 4 faces on an orientable surface of genus 2.

66066, 3288327, 85421118, 1558792200, 22555934280, 276221817810, 2979641557620, 29079129795702, 261637840342860, 2200626948631386, 17486142956133684, 132344695964811720, 960323177351524512, 6716133365837116980, 45466867668336614472, 299027167905149145858, 1916387674555902480660

Offset

7,1

Links

Table of n, a(n) for n=7..23.

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

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) ((2 n - 1)/3 Q[n - 1, f, g] + (2 n - 1)/3 Q[n - 1, f - 1, g] + (2 n - 3) (2 n - 2) (2 n - 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] (2 k - 1) (2 l - 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, 2];
Table[a[n], {n, 7, 23}] (* Jean-François Alcover, Oct 18 2018 *)

Prog

(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A288084_ser(N) = {
  my(y = A000108_ser(N+1));
  3*y*(y-1)^7*(9318*y^6 + 178328*y^5 + 177929*y^4 - 611583*y^3 + 195218*y^2 + 110388*y - 37576)/(y-2)^20;
};
Vec(A288084_ser(17))

Crossrefs

Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, A288083 f=3, this sequence, A288085 f=5, A288086 f=6, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10.

Column 4 of A269922, column 2 of A270408.

Cf. A000108.

Sequence in context: A043678 A032781 A170799 * A194430 A254192 A254185

Adjacent sequences: A288081 A288082 A288083 * A288085 A288086 A288087

Keyword

nonn

Author

Gheorghe Coserea, Jun 05 2017

Status

approved