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%I #17 Sep 08 2022 08:44:55
%S 27,730,39447,1065799,57592593,1556065810,84085146333,2271855016801,
%T 122764256053587,3316906768463650,179235729753090687,
%U 4842681610101912199,261684042675256349433,7070311833842023346890,382058523070144517081493
%N Numerators of continued fraction convergents to sqrt(731).
%H Vincenzo Librandi, <a href="/A042406/b042406.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 (0,1460,0,-1).
%F G.f.: (27 +730*x +27*x^2 -x^3)/(1 -1460*x^2 +x^4). - _Vincenzo Librandi_, Nov 23 2013
%F a(n) = 1460*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 23 2013
%t Numerator[Convergents[Sqrt[731], 30]] (* or *) CoefficientList[Series[(27 + 730 x + 27 x^2 - x^3)/(1 - 1460 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 23 2013 *)
%t LinearRecurrence[{0,1460,0,-1},{27,730,39447,1065799},20] (* _Harvey P. Dale_, Sep 16 2020 *)
%o (Magma) I:=[27, 730, 39447, 1065799]; [n le 4 select I[n] else 1460*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 23 2013
%Y Cf. A042407.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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