A042306 - OEIS

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

%S 26,339,17654,229841,11969386,155831859,8115226054,105653770561,

%T 5502111295226,71633100608499,3730423342937174,48567136558791761,

%U 2529221524400108746,32928446953760205459,1714808463119930792614

%N Numerators of continued fraction convergents to sqrt(680).

%H Vincenzo Librandi, <a href="/A042306/b042306.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 (0,678,0,-1).

%F G.f.: (26 +339*x +26*x^2 -x^3)/(1 -678*x^2 +x^4). - _Vincenzo Librandi_ Nov 21 2013

%F a(n) = 678*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 21 2013

%t Numerator[Convergents[Sqrt[680], 30]] (* or *) CoefficientList[Series[(26 + 339 x + 26 x^2 - x^3)/(1 - 678 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 21 2013 *)

%o (Magma) I:=[26, 339, 17654, 229841]; [n le 4 select I[n] else 678*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 21 2013

%Y Cf. A042307.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.