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A006295
Number of genus 1 rooted maps with 2 faces with n vertices.
(Formerly M4739)
11
10, 167, 1720, 14065, 100156, 649950, 3944928, 22764165, 126264820, 678405090, 3550829360, 18182708362, 91392185080, 452077562620, 2205359390592, 10627956019245, 50668344988068, 239250231713210, 1120028580999440, 5202779260636958, 23998704563581000, 109991785264412452
OFFSET
3,1
REFERENCES
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
W. T. Tutte, On the enumeration of planar maps, Bull. Amer. Math. Soc. 74 1968 64-74.
T. R. S. Walsh and A. B. Lehman, Counting rooted maps by genus, J. Comb. Thy B13 (1972), 122-141 and 192-218.
FORMULA
G.f.: x*(1-sqrt(1-4*x))*(11+12*x+9*sqrt(1-4*x))/(4*(4*x-1)^4). - Sean A. Irvine, Nov 14 2010
MATHEMATICA
Rest[CoefficientList[Series[(1 - Sqrt[1 - 4 x]) (11 + 12 x + 9 Sqrt[1 - 4 x]) / (4 (4 x - 1)^4), {x, 0, 40}], x]] (* Vincenzo Librandi, Jun 06 2017 *)
PROG
(PARI)
A000108_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-4*x))/(2*x);
A006295_ser(N) = {
my(y = A000108_ser(N+1)); y*(y-1)^3*(y^2 + 15*y - 6)/(y-2)^8;
};
Vec(A006295_ser(31)) \\ Gheorghe Coserea, Jun 04 2017
(PARI) my(x = 'x + O('x^60)); Vec(x*(1-sqrt(1-4*x))*(11+12*x+9*sqrt(1-4*x))/(4*(4*x-1)^4)) \\ Michel Marcus, Jun 05 2017
CROSSREFS
Rooted maps of genus 1 with n edges and f faces for 1<=f<=10: A002802(with offset 2) f=1, this sequence, A006296 f=3, A288071 f=4, A288072 f=5, A287046 f=6, A287047 f=7, A287048 f=8, A288073 f=9, A288074 f=10.
Column 2 of A269921, column 1 of A270406.
Sequence in context: A054688 A229228 A112650 * A006297 A279292 A099711
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Nov 14 2010
STATUS
approved