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A200407 The x-values in the solution to 19*x^2 - 18 = y^2. 1

%I

%S 1,9,131,209,3051,44539,71059,1037331,15143129,24159851,352689489,

%T 5148619321,8214278281,119913388929,1750515426011,2792830455689,

%U 40770199546371,595170096224419,949554140655979,13861747932377211,202356082200876449,322845614992577171

%N The x-values in the solution to 19*x^2 - 18 = y^2.

%C When are both n+1 and 19*n+1 perfect squares? This gives the equation 19*x^2-18=y^2.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,340,0,0,-1).

%F a(n)=340*a(n-3)+a(n-6), a(1)=1, a(2)=9, a(3)=131, a(4)=209, a(5)=3051, a(6)=44539.

%F G.f.: -x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1) / (x^6-340*x^3+1). - _Colin Barker_, Sep 01 2013

%e a(7)=340*209-1=71059.

%t LinearRecurrence[{0, 0, 340, 0, 0, -1}, {1, 9, 131, 209, 3051, 44539}, 50]

%o (PARI) Vec(-x*(x-1)*(x^4+10*x^3+141*x^2+10*x+1)/(x^6-340*x^3+1) + O(x^100)) \\ _Colin Barker_, Sep 01 2013

%Y Cf. A199773, A199774, A199798, A200409.

%K nonn

%O 1,2

%A _Sture Sjöstedt_, Nov 17 2011

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Last modified May 24 20:53 EDT 2019. Contains 323534 sequences. (Running on oeis4.)