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A104742 Number of rooted maps of (orientable) genus 3 containing n edges. 15
1485, 113256, 5008230, 167808024, 4721384790, 117593590752, 2675326679856, 56740864304592, 1137757854901806, 21789659909226960, 401602392805341924, 7165100439281414160, 124314235272290304540, 2105172926498512761984, 34899691847703927826500, 567797719808735191344672, 9084445205688065541367710 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,1

LINKS

T. D. Noe, Table of n, a(n) for n=6..30 (from Mednykh and Nedela)

E. A. Bender and E. R. Canfield, The number of rooted maps on an orientable surface, J. Combin. Theory, B 53 (1991), 293-299.

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

A. D. Mednykh and R. Nedela, Enumeration of unrooted maps with given genus, preprint (submitted to J. Combin. Th. B).

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, 3];

Table[a[n], {n, 6, 30}] (* Jean-Fran├žois Alcover, Jul 20 2018 *)

PROG

(PARI)

A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);

A104742_ser(N) = {

  my(y=A005159_ser(N+1));

  y*(y-1)^6*(460*y^8 - 3680*y^7 + 63055*y^6 - 198110*y^5 + 835954*y^4 - 1408808*y^3 + 1986832*y^2 - 1462400*y + 547552)/(81*(y-2)^12*(y+2)^7)

};

Vec(A104742_ser(17))  \\ Gheorghe Coserea, Jun 02 2017

CROSSREFS

Cf. A104596 (unrooted maps).

Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, A006301, this sequence, A215402, A238355, A238356, A238357, A238358, A238359, A238360.

Sequence in context: A257713 A269923 A288075 * A278853 A051260 A317593

Adjacent sequences:  A104739 A104740 A104741 * A104743 A104744 A104745

KEYWORD

nonn

AUTHOR

Valery A. Liskovets, Mar 22 2005

STATUS

approved

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Last modified March 29 17:23 EDT 2020. Contains 333116 sequences. (Running on oeis4.)