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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

%I #14 Oct 16 2018 13:57:56

%S 351683046,26225260226,993494827480,25766235457300,517592962672296,

%T 8615949311310872,123981042854132536,1587135819804394530,

%U 18451302662846918700,197822824662547694148,1979281881126113225376,18654346303702719912848,166862901890503876520320,1425340713681247480547040,11686190470805703242554960

%N a(n) is the number of rooted maps with n edges and 3 faces on an orientable surface of genus 4.

%H Sean R. Carrell, Guillaume Chapuy, <a href="http://arxiv.org/abs/1402.6300">Simple recurrence formulas to count maps on orientable surfaces</a>, arXiv:1402.6300 [math.CO], 2014.

%F 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).

%t Q[0, 1, 0] = 1; Q[n_, f_, g_] /; n < 0 || f < 0 || g < 0 = 0;

%t 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}]);

%t a[n_] := Q[n, 3, 4];

%t Table[a[n], {n, 10, 24}] (* _Jean-François Alcover_, Oct 16 2018 *)

%Y 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.

%Y Column 3 of A269924.

%Y Cf. A000108.

%K nonn

%O 10,1

%A _Gheorghe Coserea_, Jun 08 2017

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)