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 A131216 Numbers X such that 99*X^2 - 2178 is a square. 2
 11, 209, 4169, 83171, 1659251, 33101849, 660377729, 13174452731, 262828676891, 5243399085089, 104605153024889, 2086859661412691, 41632588075228931, 830564901843165929, 16569665448788089649, 330562744073918627051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..750 Index entries for linear recurrences with constant coefficients, signature (20,-1). FORMULA a(n+2) = 20*a(n+1) - a(n). a(n+1) = 10*a(n+1)+ sqrt(99*a(n)^2 -2178). G.f.: 11*z*(1-z)/(1-20*z+z^2) - Richard Choulet, Oct 09 2007 a(n) = ( 3*sqrt(11)*(10+3*sqrt(11))^(n-1) + 11*(10+3*sqrt(11))^(n-1) - 3*sqrt(11)*(10-3*sqrt(11))^(n-1) + 11*(10-3*sqrt(11))^(n-1) )/2, with n>=1 - Paolo P. Lava, Jul 15 2008 a(n) = 11*A075839(n). - R. J. Mathar, Aug 22 2012 MAPLE 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 MATHEMATICA LinearRecurrence[{20, -1}, {11, 209}, 20] (* G. C. Greubel, Dec 06 2019 *) PROG (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:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 11*x*(1-x)/(1-20*x+x^2) )); // G. C. Greubel, Dec 06 2019 (Sage) def A131216_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( 11*x*(1-x)/(1-20*x+x^2) ).list() A131216_list(20) # G. C. Greubel, Dec 06 2019 (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 CROSSREFS Cf. A083043. Sequence in context: A020518 A196849 A196699 * A034909 A081788 A060496 Adjacent sequences:  A131213 A131214 A131215 * A131217 A131218 A131219 KEYWORD nonn,easy AUTHOR Richard Choulet, Sep 27 2007 STATUS approved

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Last modified September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)