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A006301 Number of rooted genus-2 maps with n edges.
(Formerly M5120)
15
0, 0, 0, 0, 21, 966, 27954, 650076, 13271982, 248371380, 4366441128, 73231116024, 1183803697278, 18579191525700, 284601154513452, 4272100949982600, 63034617139799916, 916440476048146056, 13154166812674577412, 186700695099591735024, 2623742783421329300190, 36548087103760045010148, 505099724454854883618924 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

E. R. Canfield, Calculating the number of rooted maps on a surface, Congr. Numerantium, 76 (1990), 21-34.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. R. S. Walsh, Combinatorial Enumeration of Non-Planar Maps. Ph.D. Dissertation, Univ. of Toronto, 1971.

LINKS

T. D. Noe, Table of n, a(n) for n=0..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).

T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.

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, 2];

Table[a[n], {n, 0, 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);

A006301_ser(N) = {

  my(y=A005159_ser(N+1));

  -y*(y-1)^4*(4*y^4 - 16*y^3 + 153*y^2 - 148*y + 196)/(9*(y-2)^7*(y+2)^4);

};

concat([0, 0, 0, 0], Vec(A006301_ser(19))) \\ Gheorghe Coserea, Jun 02 2017

CROSSREFS

Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, A006300, this sequence, A104742, A215402, A238355, A238356, A238357, A238358, A238359, A238360.

Sequence in context: A012793 A015305 A101732 * A220384 A184133 A004704

Adjacent sequences:  A006298 A006299 A006300 * A006302 A006303 A006304

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and Simon Plouffe

EXTENSIONS

More terms from Joerg Arndt, Feb 26 2014

STATUS

approved

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Last modified July 20 14:01 EDT 2019. Contains 325181 sequences. (Running on oeis4.)