A288079 a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 3.

211083730, 16476937840, 647739636160, 17326957790896, 357391270819604, 6087558311398000, 89390908732820144, 1165172136542282424, 13767319160210071404, 149789855223187292608, 1518921342035154605600, 14492634832409091816640, 131114130730951689447016, 1131791523345860091265696, 9370402052804684247760928

Offset

10,1

Links

Table of n, a(n) for n=10..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) ((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, 5, 3];
Table[a[n], {n, 10, 27}] (* 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);
A288079_ser(N) = {
  my(y = A000108_ser(N+1));
  -2*y*(y-1)^10*(83904012*y^9 + 2299548501*y^8 + 8375416306*y^7 - 11663434748*y^6 - 20521873396*y^5 + 30517603222*y^4 - 3781427784*y^3 - 7908127656*y^2 + 2862038656*y - 158105248)/(y-2)^29;
};
Vec(A288079_ser(15))

Crossrefs

Rooted maps of genus 3 with n edges and f faces for 1 <= f <= 10: A288075 (f = 1), A288076 (f = 2), A288077 (f = 3), A288078 (f = 4), this sequence (f = 5), A288080 (f = 6), A288081 (f = 7), A288262 (f = 8), A288263 (f = 9), A288264 (f = 10).

Column 5 of A269923.

Cf. A000108.

Sequence in context: A092379 A233614 A105294 * A037253 A359129 A064588

Adjacent sequences: A288076 A288077 A288078 * A288080 A288081 A288082

Keyword

nonn

Author

Gheorghe Coserea, Jun 07 2017

Status

approved