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%I #22 Sep 08 2022 08:44:54
%S 1,1,8,17,127,144,4735,4879,38888,82655,617473,700128,23021569,
%T 23721697,189073448,401868593,3002153599,3404022192,111930863743,
%U 115334885935,919275065288,1953885016511,14596470180865,16550355197376,544207836496897,560758191694273
%N Denominators of continued fraction convergents to sqrt(285).
%H Vincenzo Librandi, <a href="/A041537/b041537.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 4862, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^10 -x^9 +8*x^8 -17*x^7 +127*x^6 -144*x^5 -127*x^4 -17*x^3 -8*x^2 -x -1) / ((x^4 -17*x^2 +1)*(x^8 +17*x^6 +288*x^4 +17*x^2 +1)). - _Colin Barker_, Nov 18 2013
%F a(n) = 4862*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 19 2013
%t Denominator[Convergents[Sqrt[285], 30]] (* _Harvey P. Dale_, Nov 08 2013 *)
%t CoefficientList[Series[-(x^10 - x^9 + 8 x^8 - 17 x^7 + 127 x^6 - 144 x^5 - 127 x^4 - 17 x^3 - 8 x^2 - x - 1)/((x^4 - 17 x^2 + 1) (x^8 + 17 x^6 + 288 x^4 + 17 x^2 + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 19 2013 *)
%o (Magma) I:=[1,1,8,17,127,144,4735,4879,38888,82655, 617473,700128]; [n le 12 select I[n] else 4862*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 19 2013
%Y Cf. A041536, A176104, A040268.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 18 2013
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