A288090 a(n) is the number of rooted maps with n edges and 10 faces on an orientable surface of genus 2.

7808250450, 955708437684, 56532447160536, 2200626948631386, 64232028100704156, 1511718920778951024, 30044423965980553536, 520516978029736518606, 8044640800289827566756, 112860842135424498808968, 1456882832375987896763184, 17491588653334242501297012, 197038603477850885815215480

Offset

13,1

Links

Table of n, a(n) for n=13..25.

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, 10, 2];
Table[a[n], {n, 13, 25}] (* 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);
A288090_ser(N) = {
  my(y = A000108_ser(N+1));
  6*y*(y-1)^13*(197300616213*y^12 + 2233379349250*y^11 + 1077980722075*y^10 - 16537713992125*y^9 + 7856375825902*y^8 + 29387232350368*y^7 - 33290642716432*y^6 + 994024496848*y^5 + 14078465181600*y^4 - 6737013421440*y^3 + 532103069696*y^2 + 244607984896*y - 34798091776)/(y-2)^38;
};
Vec(A288090_ser(13))

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, A288086 f=6, A288087 f=7, A288088 f=8, A288089 f=9, this sequence.

Column 10 of A269922.

Cf. A000108.

Sequence in context: A226950 A225141 A015413 * A306828 A364436 A075131

Adjacent sequences: A288087 A288088 A288089 * A288091 A288092 A288093

Keyword

nonn

Author

Gheorghe Coserea, Jun 05 2017

Status

approved