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A228206 y-values in the solution to x^2 - 13y^2 = 108. 2

%I #22 Jul 07 2022 11:35:19

%S 1,3,6,11,22,39,69,122,241,426,753,1331,2629,4647,8214,14519,28678,

%T 50691,89601,158378,312829,552954,977397,1727639,3412441,6031803,

%U 10661766,18845651,37224022,65796879,116302029,205574522,406051801,717733866,1268660553

%N y-values in the solution to x^2 - 13y^2 = 108.

%C This equation is used for worked examples in the Robertson link.

%H Colin Barker, <a href="/A228206/b228206.txt">Table of n, a(n) for n = 1..1000</a>

%H John P. Robertson, <a href="http://www.jpr2718.org/pell.pdf">Solving the generalized Pell equation x^2 - Dy^2 = N</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,11,0,0,0,-1).

%F G.f.: x*(x+1)*(x^6+2*x^5+4*x^4+7*x^3+4*x^2+2*x+1) / ((x^4-3*x^2-1)*(x^4+3*x^2-1)).

%F a(n) = 11*a(n-4)-a(n-8).

%t LinearRecurrence[{0,0,0,11,0,0,0,-1},{1,3,6,11,22,39,69,122},50] (* _Harvey P. Dale_, Jul 07 2022 *)

%o (PARI) Vec(x*(x+1)*(x^6+2*x^5+4*x^4+7*x^3+4*x^2+2*x+1)/((x^4-3*x^2-1)*(x^4+3*x^2-1)) + O(x^100))

%Y Cf. A228205

%K nonn,easy

%O 1,2

%A _Colin Barker_, Aug 16 2013

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Last modified March 28 16:00 EDT 2024. Contains 371254 sequences. (Running on oeis4.)