A042043 - OEIS

%I #17 Sep 08 2022 08:44:55

%S 1,2,3,26,29,84,3893,7870,11763,101974,113737,329448,15268345,

%T 30866138,46134483,399942002,446076485,1292094972,59882445197,

%U 121056985366,180939430563,1568572429870,1749511860433,5067596150736,234858934794289,474785465739314

%N Denominators of continued fraction convergents to sqrt(545).

%H Vincenzo Librandi, <a href="/A042043/b042043.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, 3922, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^10-2*x^9+3*x^8-26*x^7+29*x^6-84*x^5-29*x^4-26*x^3-3*x^2-2*x-1) / (x^12-3922*x^6+1). - _Colin Barker_, Nov 30 2013

%F a(n) = 3922*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Jan 13 2014

%t Denominator[Convergents[Sqrt[545], 38]] (* _Vincenzo Librandi_, Jan 13 2014 *)

%o (Magma) I:=[1,2,3,26,29,84,3893,7870,11763,101974,113737, 329448]; [n le 12 select I[n] else 3922*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Jan 13 2014

%Y Cf. A042042, A040521.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 30 2013