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A118451
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Number of rooted n-edge maps on a non-orientable genus-3 surface.
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2
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41, 1380, 31225, 592824, 10185056, 164037704, 2525186319, 37596421940, 545585129474, 7758174844664, 108518545261360, 1497384373878512, 20426386710028260, 275940187259609296, 3696482210884173349
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OFFSET
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3,1
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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.
D. M. Jackson and T. I. Visentin, An atlas of the smaller maps in orientable and nonorientable surfaces. CRC Press, Boca Raton, 2001.
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LINKS
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FORMULA
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O.g.f.: (R-1) *(R+1) *(68*R^5 +280*R^4 +588*R^3 +808*R^2 +416*R -(28*R^4+59*R^3+114*R^2+119*R+40)*sqrt(12*R*(R+2)))/ (96*R^5*(R+2)^3), where R=sqrt(1-12*x).
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MAPLE
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R := sqrt(1-12*x) ;
(R-1)*(R+1)*(68*R^5+280*R^4+588*R^3+808*R^2+416*R -(28*R^4+59*R^3+114*R^2+119*R+40)*sqrt(12*R*(R+2)))/96/R^5/(R+2)^3 ;
g := series(%, x=0, 101) ;
for n from 3 to 100 do
printf("%d %d\n", n, coeftayl(g, x=0, n)) ;
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MATHEMATICA
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R = Sqrt[1-12x];
(R-1)(R+1)(68R^5 + 280R^4 + 588R^3 + 808R^2 + 416R - (28R^4 + 59R^3 + 114R^2 + 119R + 40) Sqrt[12R(R+2)])/96/R^5/(R+2)^3 + O[x]^18 // CoefficientList[#, x]& // Drop[#, 3]& (* Jean-François Alcover, Aug 28 2019 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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