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%I #20 Sep 08 2022 08:44:55
%S 29,30,179,209,388,597,3373,3970,233633,237603,1421648,1659251,
%T 3080899,4740150,26781649,31521799,1855045991,1886567790,11287884941,
%U 13174452731,24462337672,37636790403,212646289687
%N Numerators of continued fraction convergents to sqrt(891).
%H Vincenzo Librandi, <a href="/A042722/b042722.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, 7940, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: (29 +30*x +179*x^2 +209*x^3 +388*x^4 +597*x^5 +3373*x^6 +3970*x^7 +3373*x^8 -597*x^9 +388*x^10 -209*x^11 +179*x^12 -30*x^13 +29*x^14 -x^15)/(1 -7940*x^8 +x^16). - _Vincenzo Librandi_, Dec 02 2013
%F a(n) = 7940*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 02 2013
%t Numerator[Convergents[Sqrt[891], 30]]
%t (* or *)
%t CoefficientList[Series[(29 + 30 x + 179 x^2 + 209 x^3 + 388 x^4 + 597 x^5 + 3373 x^6 + 3970 x^7 + 3373 x^8 - 597 x^9 + 388 x^10 - 209 x^11 + 179 x^12 - 30 x^13 + 29 x^14 - x^15)/(1-7940 x^8 + x^16), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 02 2013 *)
%o (Magma) I:=[29,30,179,209,388,597,3373,3970,233633,237603,1421648,1659251, 3080899,4740150,26781649,31521799]; [n le 16 select I[n] else 7940*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 02 2013
%Y Cf. A042723.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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