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%I #14 Sep 08 2022 08:44:54
%S 1,1,5,6,137,143,709,852,19453,20305,100673,120978,2762189,2883167,
%T 14294857,17178024,392211385,409389409,2029769021,2439158430,
%U 55691254481,58130412911,288212906125,346343319036
%N Denominators of continued fraction convergents to sqrt(140).
%H Vincenzo Librandi, <a href="/A041257/b041257.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 (0,0,0,142,0,0,0,-1).
%F G.f.: (1 +x +5*x^2 +6*x^3 -5*x^4 +x^5 -x^6)/(1 -142*x^4 +x^8). - _Vincenzo Librandi_, Dec 13 2013
%F a(n) = 142*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 13 2013
%t Denominator[Convergents[Sqrt[140], 30]] (* or *) CoefficientList[Series[(1 + x + 5 x^2 + 6 x^3 - 5 x^4 + x^5 - x^6)/(1 - 142 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 13 2013 *)
%o (Magma) I:=[1,1,5,6,137,143,709,852]; [n le 8 select I[n] else 142*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y Cf. A041256.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
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