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%I #21 Apr 07 2024 14:40:04
%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 G. C. Greubel, <a href="/A131216/b131216.txt">Table of n, a(n) for n = 1..750</a>
%H <a href="/index/Rec#order_02">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*(1-z)/(1-20*z+z^2) - _Richard Choulet_, Oct 09 2007
%F a(n) = 11*A075839(n). - _R. J. Mathar_, Aug 22 2012
%p 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
%t LinearRecurrence[{20, -1}, {11, 209}, 20] (* _G. C. Greubel_, Dec 06 2019 *)
%o (PARI) my(x='x+O('x^20)); Vec(11*x*(1-x)/(1-20*x+x^2)) \\ _G. C. Greubel_, Dec 06 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 11*x*(1-x)/(1-20*x+x^2) )); // _G. C. Greubel_, Dec 06 2019
%o (Sage)
%o def A131216_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 11*x*(1-x)/(1-20*x+x^2) ).list()
%o A131216_list(20) # _G. C. Greubel_, Dec 06 2019
%o (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
%Y Cf. A083043.
%K nonn,easy
%O 1,1
%A _Richard Choulet_, Sep 27 2007
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