A238356 Number of rooted maps of genus 6 containing n edges.

24325703325, 4416286056750, 425671555397220, 28948474436455224, 1558252224413413380, 70639804918689629112, 2802850363447807024080, 99911395098598706576856, 3259947795252652107008514, 98729808377337068918681196, 2805432194025270702468165744

Offset

12,1

Links

Table of n, a(n) for n=12..22.

Sean R. Carrell, Guillaume Chapuy, Simple recurrence formulas to count maps on orientable surfaces, arXiv:1402.6300 [math.CO], (19-March-2014).

S. R. Finch, An exceptional convolutional recurrence, arXiv:2408.12440 [math.CO], 22 Aug 2024.

Mathematica

T[0, 0] = 1; T[n_, g_] /; g < 0 || g > n/2 = 0; T[n_, g_] := T[n, g] = ((4 n - 2)/3 T[n - 1, g] + (2 n - 3) (2 n - 2) (2 n - 1)/12 T[n - 2, g - 1] + 1/2 Sum[(2 k - 1) (2 (n - k) - 1) T[k - 1, i] T[n - k - 1, g - i], {k, 1, n - 1}, {i, 0, g}])/((n + 1)/6);
a[n_] := T[n, 6];
Table[a[n], {n, 12, 30}] (* Jean-François Alcover, Jul 20 2018 *)

Prog

(PARI) \\ see A238396
(PARI)
A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
A238356_ser(N) = {
  my(y=A005159_ser(N+1));
  -y*(y-1)^12*(3091382412*y^20 - 61827648240*y^19 + 2494741456179*y^18 - 23821030780564*y^17 + 297709107215018*y^16 - 1898397937026724*y^15 + 11996625283021532*y^14 - 53079600835119544*y^13 + 206468965657569764*y^12 - 637634273350412392*y^11 + 1660605297373850222*y^10 - 3573247507645221112*y^9 + 6390852378647917144*y^8 - 9449999309170921856*y^7 + 11435897504002339264*y^6 - 11175919884930946304*y^5 + 8621441033651120896*y^4 - 5068129528843341824*y^3 + 2141653827725309440*y^2 - 581932716954417152*y + 76958488611567616)/(2187*(y-2)^27*(y+2)^16);
};
Vec(A238356_ser(11)) \\ Gheorghe Coserea, Jun 02 2017

Crossrefs

Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, A104742, A215402, A238355, this sequence, A238357, A238358, A238359, A238360.

Sequence in context: A129475 A172612 A293624 * A234064 A017290 A017398

Adjacent sequences: A238353 A238354 A238355 * A238357 A238358 A238359

Keyword

nonn

Author

Joerg Arndt, Feb 26 2014

Status

approved