A041217 - OEIS

%I #14 Sep 08 2022 08:44:54

%S 1,1,10,11,230,241,2399,2640,55199,57839,575750,633589,13247530,

%T 13881119,138177601,152058720,3179352001,3331410721,33162048490,

%U 36493459211,763031232710,799524691921,7958753459999,8758278151920,183124316498399,191882594650319,1910067668351270

%N Denominators of continued fraction convergents to sqrt(119).

%H Vincenzo Librandi, <a href="/A041217/b041217.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 (0,0,0,240,0,0,0,-1).

%F G.f.: (1 +x +10*x^2 +11*x^3 -10*x^4 +x^5 -x^6)/(1 -240* x^4 +x^8). - _Vincenzo Librandi_, Dec 13 2013

%F a(n) = 240*a(n-4) - a(n-8). - _Vincenzo Librandi_, Dec 13 2013

%t Denominator[Convergents[Sqrt[119], 30]] (* or *) CoefficientList[Series[(1 + x + 10 x^2 + 11 x^3 - 10 x^4 + x^5 - x^6)/(1 - 240 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 13 2013 *)

%t LinearRecurrence[{0,0,0,240,0,0,0,-1},{1,1,10,11,230,241,2399,2640},30] (* _Harvey P. Dale_, Jan 02 2020 *)

%o (Magma) I:=[1, 1, 10, 11, 230, 241, 2399, 2640]; [n le 8 select I[n] else 240*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013

%Y Cf. A041216.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Dec 13 2013