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%I #15 Sep 08 2022 08:44:55
%S 25,26,155,336,4187,8710,47737,56447,2870087,2926534,17502757,
%T 37932048,472687333,983306714,5389220903,6372527617,324015601753,
%U 330388129370,1975956248603,4282300626576,53363563767515
%N Numerators of continued fraction convergents to sqrt(668).
%H Vincenzo Librandi, <a href="/A042284/b042284.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 (0,0,0,0,0,0,0,112894,0,0,0,0,0,0,0,-1).
%F G.f.: (25 +26*x +155*x^2 +336*x^3 +4187*x^4 +8710*x^5 +47737*x^6 +56447*x^7 +47737*x^8 -8710*x^9 +4187*x^10 -336*x^11 +155*x^12 -26*x^13 +25*x^14 -x^15)/((1 -336*x^4 +x^8)*(1 +336*x^4 +x^8)). - _Vincenzo Librandi_, Nov 20 2013
%F a(n) = 112894*a(n-8) - a(n-16). - _Vincenzo Librandi_, Nov 18 2013
%t Numerator[Convergents[Sqrt[668], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 155 x^2 + 336 x^3 + 4187 x^4 + 8710 x^5 + 47737 x^6 + 56447 x^7 + 47737 x^8 - 8710 x^9 + 4187 x^10 - 336 x^11 + 155 x^12 - 26 x^13 + 25 x^14 - x^15)/(1 - 112894 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 20 2013 *)
%o (Magma) I:=[25,26,155,336,4187,8710,47737,56447,2870087,2926534,17502757, 37932048,472687333,983306714,5389220903,6372527617]; [n le 16 select I[n] else 112894*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013
%Y Cf. A042285.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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