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A131216 Numbers X such that 99*X^2-2178 is a square. 1

%I

%S 11,209,4169,83171,1659251,33101849,660377729,13174452731,

%T 262828676891,5243399085089,104605153024889,2086859661412691,

%U 41632588075228931,830564901843165929,16569665448788089649,330562744073918627051

%N Numbers X such that 99*X^2-2178 is a square.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (20,-1).

%F a(n+2)=20*a(n+1)-a(n).

%F a(n+1)=10*a(n+1)+ sqrt(99*a(n)^2-2178).

%F G.f.: (11*z-11*z^2)/(1-20*z+z^2) - _Richard Choulet_, Oct 09 2007

%F a(n)=(3/2)*[10+3*sqrt(11)]^(n-1)*sqrt(11)+(11/2)*[10+3*sqrt(11)]^(n-1)-(3/2)*sqrt(11)*[10-3 *sqrt(11)]^(n-1)+(11/2)*[10-3*sqrt(11)]^(n-1), with n>=1 - _Paolo P. Lava_, Jul 15 2008

%F a(n) = 11*A075839(n-1). - _R. J. Mathar_, Aug 22 2012

%Y Cf. A083043.

%K nonn,easy

%O 1,1

%A _Richard Choulet_, Sep 27 2007

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Last modified June 16 06:46 EDT 2019. Contains 324145 sequences. (Running on oeis4.)