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%I #16 Sep 08 2022 08:44:55
%S 26,105,5486,22049,1152034,4630185,241921654,972316801,50802395306,
%T 204181898025,10668261092606,42877226268449,2240284027051954,
%U 9004013334476265,470448977419817734,1890799923013747201
%N Numerators of continued fraction convergents to sqrt(689).
%H Vincenzo Librandi, <a href="/A042324/b042324.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 210, 0, -1).
%F G.f.: (26 +105*x +26*x^2 -x^3)/(1 -210*x^2 +x^4). - _Vincenzo Librandi_ Nov 21 2013
%F a(n) = 210*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 21 2013
%t Numerator[Convergents[Sqrt[689], 30]] (* or *) CoefficientList[Series[(26 + 105 x + 26 x^2 - x^3)/(1 -210 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 21 2013 *)
%t LinearRecurrence[{0,210,0,-1},{26,105,5486,22049},20] (* _Harvey P. Dale_, May 12 2017 *)
%o (Magma) I:=[26, 105, 5486, 22049]; [n le 4 select I[n] else 210*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 21 2013
%Y Cf. A042325.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.