A287048 a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 1.

291720, 22764165, 875029804, 22620890127, 448035881592, 7302676928666, 102432266545800, 1274461449989715, 14373136466094880, 149314477245194262, 1446563778096423816, 13196809961724011350, 114253624700659216080, 944690705838217837620, 7498935691376059259344, 57398464959432306918747

Offset

9,1

Links

Table of n, a(n) for n=9..24.

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, 8, 1];
Table[a[n], {n, 9, 25}] (* 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);
A287048_ser(N) = {
  my(y = A000108_ser(N+1));
  y*(y-1)^9*(9370183*y^8 + 52321971*y^7 - 83853806*y^6 - 93946092*y^5 + 189910936*y^4 - 57493776*y^3 - 31383264*y^2 + 16878912*y - 1513344)/(y-2)^26;
};
Vec(A287048_ser(16))

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, A287046 f=6, A287047 f=7, this sequence, A288073 f=9, A288074 f=10.

Column 8 of A269921; column 1 of A270412.

Cf. A000108.

Sequence in context: A252992 A253532 A233988 * A168500 A104328 A219318

Adjacent sequences: A287045 A287046 A287047 * A287049 A287050 A287051

Keyword

nonn

Author

Gheorghe Coserea, Jun 04 2017

Status

approved