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%I #17 Sep 08 2022 08:44:55
%S 24,25,224,249,12176,12425,111576,124001,6063624,6187625,55564624,
%T 61752249,3019672576,3081424825,27671071176,30752496001,1503790879224,
%U 1534543375225,13780137881024,15314681256249
%N Numerators of continued fraction convergents to sqrt(620).
%H Vincenzo Librandi, <a href="/A042190/b042190.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, 498, 0, 0, 0, -1).
%F G.f.: (24 +25*x +224*x^2 +249*x^3 +224*x^4 -25*x^5 +24*x^6 -x^7)/(1 -498*x^4 +x^8). - _Vincenzo Librandi_, Nov 18 2013
%F a(n) = 498*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 18 2013
%t Numerator[Convergents[Sqrt[620], 30]] (* or *) CoefficientList[Series[(24 + 25 x + 224 x^2 + 249 x^3 + 224 x^4 - 25 x^5 + 24 x^6 - x^7)/(1 - 498 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 18 2013 *)
%t LinearRecurrence[{0,0,0,498,0,0,0,-1},{24,25,224,249,12176,12425,111576,124001},20] (* _Harvey P. Dale_, Dec 15 2014 *)
%o (Magma) I:=[24, 25, 224, 249, 12176, 12425, 111576, 124001]; [n le 8 select I[n] else 498*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013
%Y Cf. A042191.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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