A288263 - OEIS

%I #15 Oct 17 2018 05:23:19

%S 1384928666550,176357530955320,10933959720960760,447708887118504600,

%T 13767319160210071404,341505418008822731328,7151648337964982801760,

%U 130468023103972196647776,2121333601263313429701060,31276917257222840819283888,423834000658990977141751472,5335660046838578422013157200

%N a(n) is the number of rooted maps with n edges and 9 faces on an orientable surface of genus 3.

%H Gheorghe Coserea, <a href="/A288263/a288263.txt">The g.f. as a rational function of y=A000108(x)</a>

%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.

%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, 9, 3];

%t Table[a[n], {n, 14, 25}] (* _Jean-François Alcover_, Oct 17 2018 *)

%Y 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, A288262 f=8, this sequence, A288264 f=10.

%Y Column 9 of A269923.

%Y Cf. A000108.

%K nonn

%O 14,1

%A _Gheorghe Coserea_, Jun 07 2017