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A006300
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Number of rooted maps with n edges on torus.
(Formerly M5097)
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17
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1, 20, 307, 4280, 56914, 736568, 9370183, 117822512, 1469283166, 18210135416, 224636864830, 2760899996816, 33833099832484, 413610917006000, 5046403030066927, 61468359153954656, 747672504476150374, 9083423595292949240, 110239596847544663002, 1336700736225591436496, 16195256987701502444284
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OFFSET
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2,2
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REFERENCES
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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.
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LINKS
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FORMULA
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G.f.: (R-1)^2/(12*R^2*(R+2)) where R=sqrt(1-12*x); a(n) is asymptotic to 12^n/24. - Pab Ter (pabrlos2(AT)yahoo.com), Nov 07 2005
a(n) = Sum_{k=0..n-2} 2^(n-3-k)*(3^(n-1)-3^k)*binomial(n+k,k). - Ruperto Corso, Dec 18 2011
D-finite with recurrence: n*a(n) +22*(-n+1)*a(n-1) +4*(22*n-65)*a(n-2) +96*(5*n-4)*a(n-3) +576*(-2*n+7)*a(n-4)=0. - R. J. Mathar, Feb 20 2020
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MAPLE
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R:=sqrt(1-12*x): seq(coeff(convert(series((R-1)^2/(12*R^2*(R+2)), x, 50), polynom), x, n), n=2..25); (Pab Ter)
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MATHEMATICA
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Drop[With[{c=Sqrt[1-12x]}, CoefficientList[Series[(c-1)^2/(12c^2 (c+2)), {x, 0, 30}], x]], 2] (* Harvey P. Dale, Jun 14 2011 *)
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PROG
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(PARI)
A005159_ser(N) = my(x='x+O('x^(N+1))); (1 - sqrt(1-12*x))/(6*x);
A006300_ser(N) = my(y = A005159_ser(N+1)); y*(y-1)^2/(3*(y-2)^2*(y+2));
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CROSSREFS
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Rooted maps with n edges of genus g for 0 <= g <= 10: A000168, this sequence, A006301, A104742, A215402, A238355, A238356, A238357, A238358, A238359, A238360.
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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Bender et al. give 20 terms.
More terms from Pab Ter (pabrlos2(AT)yahoo.com), Nov 07 2005
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STATUS
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approved
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