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%I #17 Sep 08 2022 08:44:55
%S 25,626,31325,783751,39218875,981255626,49102000175,1228531260001,
%T 61475665000225,1538120156265626,76967483478281525,
%U 1925725207113303751,96363227839143469075,2411006421185700030626,120646684287124145000375
%N Numerators of continued fraction convergents to sqrt(627).
%H Vincenzo Librandi, <a href="/A042202/b042202.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 (0,1252,0,-1).
%F G.f.: (25 +626*x +25*x^2 -x^3)/(1 -1252*x^2 +x^4). - _Vincenzo Librandi_, Nov 19 2013
%F a/n) = 1252*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 19 2013
%t Numerator[Convergents[Sqrt[627], 20]] (* _Harvey P. Dale_, Oct 20 2012 *)
%t CoefficientList[Series[(25 + 626 x + 25 x^2 - x^3)/(x^4 - 1252 x^2 + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Nov 19 2013 *)
%o (Magma) I:=[25,626,31325,783751]; [n le 4 select I[n] else 1252*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 19 2013
%Y Cf. A042203.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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