|
%I #19 Sep 08 2022 08:44:55
%S 1,1,2,3,8,11,19,30,1279,1309,2588,3897,10382,14279,24661,38940,
%T 1660141,1699081,3359222,5058303,13475828,18534131,32009959,50544090,
%U 2154861739,2205405829,4360267568,6565673397,17491614362,24057287759,41548902121,65606189880
%N Denominators of continued fraction convergents to sqrt(468).
%H Vincenzo Librandi, <a href="/A041893/b041893.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 (0,0,0,0,0,0,0,1298,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+10*x^4+1) / ((x^8-36*x^4-1)*(x^8+36*x^4-1)). - _Colin Barker_, Nov 26 2013
%F a(n) = 1298*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 26 2013
%t Denominator[Convergents[Sqrt[468], 50]] (* _Harvey P. Dale_, Sep 19 2011 *)
%t CoefficientList[Series[-(x^14 - x^13 + 2 x^12 - 3 x^11 + 8 x^10 - 11 x^9 + 19 x^8 - 30 x^7 - 19 x^6 - 11 x^5 - 8 x^4 - 3 x^3 - 2 x^2 - x - 1)/(x^16 - 1298 x^8 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 26 2013 *)
%o (Magma) I:=[1,1,2,3,8,11,19,30,1279,1309,2588,3897, 10382,14279,24661,38940]; [n le 16 select I[n] else 1298*Self(n-8)-Self(n-16): n in [1..50]]; // _Vincenzo Librandi_, Dec 26 2013
%Y Cf. A041892, A040446.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 26 2013
|
