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A288262
a(n) is the number of rooted maps with n edges and 8 faces on an orientable surface of genus 3.
10
174437377400, 19925913354061, 1115525500250760, 41491242915292306, 1165172136542282424, 26522236056202555206, 511895831411154922176, 8640883781524178188980, 130468023103972196647776, 1792206112041706943912462, 22695416350294243544684240, 267740228837597817351215676
OFFSET
13,1
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) ((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, 3];
Table[a[n], {n, 13, 24}] (* 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);
A288262_ser(N) = {
my(y = A000108_ser(N+1));
y*(y-1)^13*(2675326679856*y^12 + 54684388381464*y^11 + 178122315841075*y^10 - 372236561648447*y^9 - 717438005317146*y^8 + 1482970059363466*y^7 - 17264319660476*y^6 - 1294789702753096*y^5 + 770104389507952*y^4 - 4493523304288*y^3 - 105563098094272*y^2 + 24298454684800*y - 895286303488)/(y-2)^38;
};
Vec(A288262_ser(12))
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, A288079 f=5, A288080 f=6, A288081 f=7, this sequence, A288263 f=9, A288264 f=10.
Column 8 of A269923.
Cf. A000108.
Sequence in context: A197633 A339122 A105295 * A233624 A104800 A217091
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 07 2017
STATUS
approved