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%I #17 Sep 08 2022 08:44:54
%S 20,21,41,62,2521,2583,5104,7687,312584,320271,632855,953126,38757895,
%T 39711021,78468916,118179937,4805666396,4923846333,9729512729,
%U 14653359062,595863875209,610517234271,1206381109480
%N Numerators of continued fraction convergents to sqrt(427).
%H Vincenzo Librandi, <a href="/A041812/b041812.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 124, 0, 0, 0, -1).
%F G.f.: (20+21*x+41*x^2+62*x^3+41*x^4-21*x^5+20*x^6-x^7)/(1-124*x^4+x^8). - _Vincenzo Librandi_, Nov 09 2013
%F a(n) = 124*a(n-4)-a(n-8). - _Vincenzo Librandi_, Nov 09 2013
%t Numerator[Convergents[Sqrt[427], 30]] (* or *) CoefficientList[Series[(20 + 21 x + 41 x^2 + 62 x^3 + 41 x^4 - 21 x^5 + 20 x^6 - x^7)/(1 - 124 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 09 2013 *)
%o (Magma) I:=[20,21,41,62,2521,2583,5104,7687]; [n le 8 select I[n] else 124*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Nov 09 2013
%Y Cf. A041813.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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