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A288079
a(n) is the number of rooted maps with n edges and 5 faces on an orientable surface of genus 3.
10
211083730, 16476937840, 647739636160, 17326957790896, 357391270819604, 6087558311398000, 89390908732820144, 1165172136542282424, 13767319160210071404, 149789855223187292608, 1518921342035154605600, 14492634832409091816640, 131114130730951689447016, 1131791523345860091265696, 9370402052804684247760928
OFFSET
10,1
LINKS
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
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 07 2017
STATUS
approved