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A131216
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Numbers X such that 99*X^2 - 2178 is a square.
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2
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11, 209, 4169, 83171, 1659251, 33101849, 660377729, 13174452731, 262828676891, 5243399085089, 104605153024889, 2086859661412691, 41632588075228931, 830564901843165929, 16569665448788089649, 330562744073918627051
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n+2) = 20*a(n+1) - a(n).
a(n+1) = 10*a(n+1)+ sqrt(99*a(n)^2 -2178).
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MAPLE
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seq(coeff(series(11*x*(1-x)/(1-20*x+x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Dec 06 2019
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MATHEMATICA
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LinearRecurrence[{20, -1}, {11, 209}, 20] (* G. C. Greubel, Dec 06 2019 *)
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PROG
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(PARI) my(x='x+O('x^20)); Vec(11*x*(1-x)/(1-20*x+x^2)) \\ G. C. Greubel, Dec 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 11*x*(1-x)/(1-20*x+x^2) )); // G. C. Greubel, Dec 06 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 11*x*(1-x)/(1-20*x+x^2) ).list()
(GAP) a:=[11, 209];; for n in [3..20] do a[n]:=20*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 06 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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