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A042660 Numerators of continued fraction convergents to sqrt(860). 2

%I

%S 29,88,1261,3871,225779,681208,9762691,29969281,1747980989,5273912248,

%T 75582752461,232022169631,13532868591059,40830627942808,

%U 585161659790371,1796315607313921,104771466883997789,316110716259307288

%N Numerators of continued fraction convergents to sqrt(860).

%H Vincenzo Librandi, <a href="/A042660/b042660.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 (0,0,0,7742,0,0,0,-1).

%F G.f.: (29 +88*x +1261*x^2 +3871*x^3 +1261*x^4 -88*x^5 +29*x^6 -x^7)/(1 -7742*x^4 +x^8). - _Vincenzo Librandi_, Nov 30 2013

%F a(n) = 7742*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 30 2013

%t Numerator[Convergents[Sqrt[860], 30]] (* _Harvey P. Dale_, Mar 04 2013 *)

%t CoefficientList[Series[(29 + 88 x + 1261 x^2 + 3871 x^3 + 1261 x^4 - 88 x^5 + 29 x^6 - x^7)/(1 - 7742 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 30 2013 *)

%o (MAGMA) I:=[29, 88, 1261, 3871, 225779, 681208, 9762691, 29969281]; [n le 8 select I[n] else 7742*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 30 2013

%Y Cf. A042661.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified June 25 12:01 EDT 2019. Contains 324352 sequences. (Running on oeis4.)