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%I #15 Sep 08 2022 08:44:55
%S 25,51,2575,5201,262625,530451,26785175,54100801,2731825225,
%T 5517751251,278619387775,562756526801,28416445727825,57395647982451,
%U 2898198844850375,5853793337683201,295587865729010425,597029524795704051
%N Numerators of continued fraction convergents to sqrt(650).
%H Vincenzo Librandi, <a href="/A042248/b042248.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 (0,102,0,-1).
%F G.f.: (1 + x)*(25 + 26*x - x^2)/((1 - 10*x - x^2)*(1 + 10*x - x^2)) = (25 + 51*x + 25*x^2 - x^3)/(1 - 102*x^2 + x^4). - _Vincenzo Librandi_, Nov 20 2013
%F a(n) = 102*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 20 2013
%t Numerator[Convergents[Sqrt[650], 30]] (* or *) CoefficientList[Series[(25 + 51 x + 25 x^2 - x^3)/(1 - 102 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 20 2013 *)
%o (Magma) I:=[25,51,2575,5201]; [n le 4 select I[n] else 102*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 20 2013
%Y Cf. A042249.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.