login
A288276
a(n) is the number of rooted maps with n edges and 6 faces on an orientable surface of genus 4.
12
1480593013900, 160576594766588, 8615949311310872, 309197871098871838, 8419549939292302908, 186553519919803261860, 3515647035511186627416, 58089920897558352891672, 860337164444236894357488, 11612741439751867739074432, 144715531380208437909370144, 1682205432436689960841795876
OFFSET
13,1
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)^13*(1208305403982*y^12 + 42344287039512*y^11 + 283047148578040*y^10 + 47183718440672*y^9 - 1618438221531593*y^8 + 617910272368381*y^7 + 2488374601412831*y^6 - 2268379207704481*y^5 - 116197489174642*y^4 + 764144804102008*y^3 - 252877960850800*y^2 + 8651012216320*y + 3769026206720)/(y-2)^38, 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, 6, 4];
Table[a[n], {n, 13, 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, A288273 f=3, A288274 f=4, A288275 f=5, this sequence, A288277 f=7, A288278 f=8, A288279 f=9, A288280 f=10.
Column 6 of A269924.
Cf. A000108.
Sequence in context: A335085 A213601 A213646 * A246251 A320943 A248892
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Jun 08 2017
STATUS
approved