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A288273
a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 4.
10
351683046, 26225260226, 993494827480, 25766235457300, 517592962672296, 8615949311310872, 123981042854132536, 1587135819804394530, 18451302662846918700, 197822824662547694148, 1979281881126113225376, 18654346303702719912848, 166862901890503876520320, 1425340713681247480547040, 11686190470805703242554960
OFFSET
10,1
LINKS
Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], 2014.
FORMULA
G.f.: -2*y*(y-1)^10*(12317877*y^9 + 793781118*y^8 + 6094043038*y^7 + 2216299748*y^6 - 23375789497*y^5 + 7963356801*y^4 + 15368481377*y^3 - 10027219339*y^2 + 877859200*y + 252711200)/(y-2)^29, where y=A000108(x).
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, 3, 4];
Table[a[n], {n, 10, 24}] (* Jean-François Alcover, Oct 16 2018 *)
CROSSREFS
Rooted maps of genus 4 with n edges and f faces for 1<=f<=10: A288271 f=1, A288272 f=2, this sequence, A288274 f=4, A288275 f=5, A288276 f=6, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.
Column 3 of A269924.
Cf. A000108.
Sequence in context: A257384 A186628 A032757 * A219271 A167517 A227642
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved