login
A288086
a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 2.
9
4390386, 313530000, 11270290416, 276221817810, 5235847653036, 82234427131416, 1117259292848016, 13518984452463630, 148755268498286436, 1511718920778951024, 14358354462488121408, 128656798319026864068, 1095747149735034238680, 8924653047010981590288, 69866689045523025725664
OFFSET
9,1
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, 6, 2];
Table[a[n], {n, 9, 23}] (* 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);
A288086_ser(N) = {
my(y = A000108_ser(N+1));
6*y*(y-1)^9*(2211997*y^8 + 32071458*y^7 + 27414609*y^6 - 154896511*y^5 + 58087530*y^4 + 94331624*y^3 - 68497296*y^2 + 8775424*y + 1232896)/(y-2)^26;
};
Vec(A288086_ser(15))
CROSSREFS
Rooted maps of genus 2 with n edges and f faces for 1<=f<=10: A006298 f=1, A288082 f=2, A288083 f=3, A288084 f=4, A288085 f=5, this sequence, A288087 f=7, A288088 f=8, A288089 f=9, A288090 f=10.
Column 6 of A269922, column 2 of A270410.
Cf. A000108.
Sequence in context: A254305 A237537 A276323 * A210297 A019288 A237910
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 05 2017
STATUS
approved