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Numerators of continued fraction convergents to sqrt(690).
2

%I #12 Sep 08 2022 08:44:55

%S 26,79,105,289,394,1471,76886,232129,309015,850159,1159174,4327681,

%T 226198586,682923439,909122025,2501167489,3410289514,12732036031,

%U 665476163126,2009160525409,2674636688535,7358433902479

%N Numerators of continued fraction convergents to sqrt(690).

%H Vincenzo Librandi, <a href="/A042326/b042326.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,2942,0,0,0,0,0,-1).

%F G.f.: -(x^11 -26*x^10 +79*x^9 -105*x^8 +289*x^7 -394*x^6 -1471*x^5 -394*x^4 -289*x^3 -105*x^2 -79*x -26)/(x^12 -2942*x^6 +1). - _Vincenzo Librandi_ Nov 21 2013

%F a(n) = 2942*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 21 2013

%t Numerator[Convergents[Sqrt[690], 30]] (* or *) CoefficientList[Series[-(x^11 - 26 x^10 + 79 x^9 - 105 x^8 + 289 x^7 - 394 x^6 - 1471 x^5 - 394 x^4 - 289 x^3 - 105 x^2 - 79 x - 26)/(x^12 - 2942 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 21 2013 *)

%o (Magma) I:=[26, 79, 105, 289, 394, 1471, 76886, 232129, 309015, 850159, 1159174, 4327681]; [n le 12 select I[n] else 2942*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 21 2013

%Y Cf. A042327.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.