A287046 a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 1.

12012, 649950, 17970784, 344468530, 5188948072, 65723863196, 729734918432, 7302676928666, 67173739068760, 576218752277476, 4660202610532480, 35839052357422132, 263868150558327376, 1870153808268516280, 12816868756802256832, 85256107136168684650, 552171259884681058744

Offset

7,1

Links

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

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

Sean R. Carrell and Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, Journal of Combinatorial Theory, Series A, 133 (2015), 58-75.

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, 6, 1];
Table[a[n], {n, 7, 23}] (* Jean-François Alcover, Oct 17 2018 *)

Prog

(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A287046_ser(N) = {
  my(y = A000108_ser(N+1));
  2*y*(y-1)^7*(28457*y^6 + 179171*y^5 - 222214*y^4 - 172512*y^3 + 257232*y^2 - 59904*y - 4224)/(y-2)^20;
};
Vec(A287046_ser(17))

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, A288072 f=5, this sequence, A287047 f=7, A287048 f=8, A288073 f=9, A288074 f=10.

Column 6 of A269921, column 1 of A270410.

Cf. A000108.

Sequence in context: A236607 A156713 A183059 * A235308 A064966 A292815

Adjacent sequences: A287043 A287044 A287045 * A287047 A287048 A287049

Keyword

nonn

Author

Gheorghe Coserea, Jun 04 2017

Status

approved