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%I #18 Sep 08 2022 08:44:55
%S 28,785,43988,1232449,69061132,1934944145,108425933252,3037861075201,
%T 170228646144508,4769439953121425,267258866020944308,
%U 7488017688539562049,419596249424236419052,11756183001567159295505
%N Numerators of continued fraction convergents to sqrt(786).
%H Vincenzo Librandi, <a href="/A042514/b042514.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 (0,1570,0,-1).
%F a(n) = (28 + 785*x + 28*x^2 - x^3)/(1 - 1570*x^2 + x^4). - _Vincenzo Librandi_, Nov 26 2013
%F a(n) = 1570*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 26 2013
%t Numerator[Convergents[Sqrt[786], 30]] (* or *) CoefficientList[Series[(28 + 785 x + 28 x^2 - x^3)/(1 - 1570 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 25 2013 *)
%t LinearRecurrence[{0,1570,0,-1},{28,785,43988,1232449},20] (* _Harvey P. Dale_, Feb 24 2015 *)
%o (Magma) I:=[28, 785, 43988, 1232449]; [n le 4 select I[n] else 1570*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 26 2013
%Y Cf. A042515.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_
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