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%I #13 Sep 08 2022 08:44:55
%S 27,28,83,111,6077,6188,18453,24641,1349067,1373708,4096483,5470191,
%T 299486797,304956988,909400773,1214357761,66484719867,67699077628,
%U 201882875123,269581952751,14759308323677,15028890276428
%N Numerators of continued fraction convergents to sqrt(770).
%H Vincenzo Librandi, <a href="/A042484/b042484.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 (0,0,0,222,0,0,0,-1).
%F G.f.: (27 +28*x +83*x^2 +111*x^3 +83*x^4 -28*x^5 +27*x^6 -x^7)/(1 -222*x^4 +x^8). - _Vincenzo Librandi_, Nov 26 2013
%F a(n) = 222*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 26 2013
%t Numerator[Convergents[Sqrt[770], 30]] (* or *) CoefficientList[Series[(27 + 28 x + 83 x^2 + 111 x^3 + 83 x^4 - 28 x^5 + 27 x^6 - x^7)/(1 - 222 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 25 2013 *)
%o (Magma) I:=[27, 28, 83, 111, 6077, 6188, 18453, 24641]; [n le 8 select I[n] else 222*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 26 2013
%Y Cf. A042485.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.