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%I #17 Sep 08 2022 08:44:55
%S 30,31,61,153,214,581,795,1376,83355,84731,168086,420903,588989,
%T 1598881,2187870,3786751,229392930,233179681,462572611,1158324903,
%U 1620897514,4400119931,6021017445,10421137376,631289260005,641710397381,1272999657386,3187709712153
%N Numerators of continued fraction convergents to sqrt(935).
%H Vincenzo Librandi, <a href="/A042808/b042808.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 2752, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (30 +31*x +61*x^2 +153*x^3 +214*x^4 +581*x^5 +795*x^6 +1376*x^7 +795*x^8 -581*x^9 +214*x^10 -153*x^11 +61*x^12 -31*x^13 +30*x^14 -x^15)/(1 -2752*x^8 +x^16). - _Vincenzo Librandi_, Dec 05 2013
%F a(n) = 2752*a(n-8) - a(n-16) - _Vincenzo Librandi_, Dec 05 2013
%t Numerator[Convergents[Sqrt[935], 30]] (* or *) CoefficientList[Series[(30 + 31 x + 61 x^2 + 153 x^3 + 214 x^4 + 581 x^5 + 795 x^6 + 1376 x^7 + 795 x^8 - 581 x^9 + 214 x^10 - 153 x^11 + 61 x^12 - 31 x^13 + 30 x^14 - x^15)/(1 - 2752 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 05 2013 *)
%o (Magma) I:=[30, 31, 61, 153, 214, 581, 795, 1376, 83355, 84731, 168086, 420903, 588989, 1598881, 2187870, 3786751]; [n le 16 select I[n] else 2752*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 05 2013
%Y Cf. A042809.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
%E More terms from _Vincenzo Librandi_, Dec 05 2013
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