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A042264 Numerators of continued fraction convergents to sqrt(658). 2

%I

%S 25,26,51,77,513,590,1103,1693,85753,87446,173199,260645,1737069,

%T 1997714,3734783,5732497,290359633,296092130,586451763,882543893,

%U 5881715121,6764259014,12645974135,19410233149

%N Numerators of continued fraction convergents to sqrt(658).

%H Vincenzo Librandi, <a href="/A042264/b042264.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 3386, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: (25 +26*x +51*x^2 +77*x^3 +513*x^4 +590*x^5 +1103*x^6 +1693*x^7 +1103*x^8 -590*x^9 +513*x^10 -77*x^11 +51*x^12 -26*x^13 +25*x^14 -x^15)/(1 -3386*x^8 +x^16). - _Vincenzo Librandi_, Nov 20 2013

%F a(n) = 3386*a(n-8) - a(n-16). - _Vincenzo Librandi_, Nov 18 2013

%t Numerator[Convergents[Sqrt[658], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 51 x^2 + 77 x^3 + 513 x^4 + 590 x^5 + 1103 x^6 + 1693 x^7 + 1103 x^8 - 590 x^9 + 513 x^10 - 77 x^11 + 51 x^12 - 26 x^13 + 25 x^14 - x^15)/(1 - 3386 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 20 2013 *)

%o (MAGMA) I:=[25, 26, 51, 77, 513, 590, 1103, 1693, 85753, 87446, 173199, 260645, 1737069, 1997714, 3734783, 5732497]; [n le 16 select I[n] else 3386*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013

%Y Cf. A042265.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified September 20 00:26 EDT 2020. Contains 337215 sequences. (Running on oeis4.)