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%I #12 Sep 08 2022 08:44:55
%S 26,157,183,340,4263,4603,8866,57799,3014414,18144283,21158697,
%T 39302980,492794457,532097437,1024891894,6681448801,348460229546,
%U 2097442826077,2445903055623,4543345881700,56966053636023
%N Numerators of continued fraction convergents to sqrt(684).
%H Vincenzo Librandi, <a href="/A042314/b042314.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 (0,0,0,0,0,0,0,115598,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^15 -26*x^14 +157*x^13 -183*x^12 +340*x^11 -4263*x^10 +4603*x^9 -8866*x^8 -57799*x^7 -8866*x^6 -4603*x^5 -4263*x^4 -340*x^3 -183*x^2 -157*x -26)/(x^16 -115598*x^8 +1). - _Vincenzo Librandi_ Nov 21 2013
%F a(n) = 115598*a(n-8) - a(n-16), - _Vincenzo Librandi_, Nov 21 2013
%t Numerator[Convergents[Sqrt[684], 30]] (* or *) CoefficientList[Series[-(x^15 - 26 x^14 + 157 x^13 - 183 x^12 + 340 x^11 - 4263 x^10 + 4603 x^9 - 8866 x^8 - 57799 x^7 - 8866 x^6 - 4603 x^5 - 4263 x^4 - 340 x^3 - 183 x^2 - 157 x - 26)/(x^16 - 115598 x^8 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 21 2013 *)
%o (Magma) I:=[26, 157, 183, 340, 4263, 4603, 8866, 57799, 3014414, 18144283, 21158697, 39302980, 492794457, 532097437, 1024891894, 6681448801]; [n le 16 select I[n] else 115598*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Nov 21 2013
%Y Cf. A042315.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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