A288072 a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 1.

2310, 100156, 2278660, 36703824, 472592916, 5188948072, 50534154408, 448035881592, 3682811916980, 28442316247080, 208462422428152, 1461307573813824, 9857665477085832, 64309102366765200, 407372683115470800, 2514120288996270024, 15159074541052024308, 89512241718624419624

Offset

6,1

Links

Table of n, a(n) for n=6..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, 5, 1];
Table[a[n], {n, 6, 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);
A288072_ser(N) = {
  my(y = A000108_ser(N+1));
  -2*y*(y-1)^6*(2140*y^5 + 14751*y^4 - 15604*y^3 - 8820*y^2 + 10176*y - 1488)/(y-2)^17;
};
Vec(A288072_ser(18))

Crossrefs

Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, A006295 f=2, A006296 f=3, A288071 f=4, this sequence, A287046 f=6, A287047 f=7, A287048 f=8, A288073 f=9, A288074 f=10.

Column 5 of A269921.

Cf. A000108.

Sequence in context: A147572 A046303 A046403 * A087978 A261210 A020435

Adjacent sequences: A288069 A288070 A288071 * A288073 A288074 A288075

Keyword

nonn

Author

Gheorghe Coserea, Jun 05 2017

Status

approved