%I #17 Sep 08 2022 08:44:55
%S 29,175,379,2449,142421,856975,1856371,11995201,697578029,4197463375,
%T 9092504779,58752492049,3416737043621,20559174753775,44535086551171,
%U 287769694060801,16735177342077629,100698833746526575
%N Numerators of continued fraction convergents to sqrt(850).
%H Vincenzo Librandi, <a href="/A042640/b042640.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, 4898, 0, 0, 0, -1).
%F G.f.: (29 +175*x +379*x^2 +2449*x^3 +379*x^4 -175*x^5 +29*x^6 -x^7)/(1 -4898*x^4 +x^8). - _Vincenzo Librandi_, Nov 30 2013
%F a(n) = 4898*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 30 2013
%t Numerator[Convergents[Sqrt[850], 30]] (* _Harvey P. Dale_, Oct 27 2011 *)
%t CoefficientList[Series[(29 + 175 x + 379 x^2 + 2449 x^3 + 379 x^4 - 175 x^5 + 29 x^6 - x^7)/(1 - 4898 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 30 2013 *)
%o (Magma) I:=[29, 175, 379, 2449, 142421, 856975, 1856371, 11995201]; [n le 8 select I[n] else 4898*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 30 2013
%Y Cf. A042641.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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