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%I #17 Sep 08 2022 08:44:55
%S 29,30,269,299,17611,17910,160891,178801,10531349,10710150,96212549,
%T 106922699,6297729091,6404651790,57534943411,63939595201,
%U 3766031465069,3829971060270,34405799947229,38235771007499
%N Numerators of continued fraction convergents to sqrt(894).
%H Vincenzo Librandi, <a href="/A042728/b042728.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 598, 0, 0, 0, -1).
%F G.f.: (29 +30*x +269*x^2 +299*x^3 +269*x^4 -30*x^5 +29*x^6 -x^7)/(1 -598*x^4 +x^8). - _Vincenzo Librandi_, Dec 03 2013
%F a(n) = 598*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 03 2013
%t Numerator[Convergents[Sqrt[894], 30]] (* or *) CoefficientList[Series[(29 + 30 x + 269 x^2 + 299 x^3 + 269 x^4 - 30 x^5 + 29 x^6 - x^7)/(1 - 598 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 03 2013 *)
%t LinearRecurrence[{0,0,0,598,0,0,0,-1},{29,30,269,299,17611,17910,160891,178801},30] (* _Harvey P. Dale_, Jul 24 2019 *)
%o (Magma) I:=[29, 30, 269, 299, 17611, 17910, 160891, 178801]; [n le 8 select I[n] else 598*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2013
%Y Cf. A042729.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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