A041477 - OEIS

%I #17 Mar 03 2024 16:04:32

%S 1,1,15,16,495,511,7649,8160,252449,260609,3900975,4161584,128748495,

%T 132910079,1989489601,2122399680,65661480001,67783879681,

%U 1014635795535,1082419675216,33487226052015,34569645727231,517462266233249,552031911960480,17078419625047649

%N Denominators of continued fraction convergents to sqrt(254).

%H Vincenzo Librandi, <a href="/A041477/b041477.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 (0,0,0,510,0,0,0,-1).

%F G.f.: -(x^2-x-1)*(x^4+16*x^2+1) / (x^8-510*x^4+1). - _Colin Barker_, Nov 18 2013

%F a(n) = 510*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Dec 18 2013

%t Denominator[Convergents[Sqrt[254], 30]] (* _Vincenzo Librandi_, Dec 18 2013 *)

%t LinearRecurrence[{0,0,0,510,0,0,0,-1},{1,1,15,16,495,511,7649,8160},30] (* _Harvey P. Dale_, Mar 03 2024 *)

%o (Magma) I:=[1,1,15,16,495,511,7649,8160]; [n le 8 select I[n] else 510*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 18 2013

%Y Cf. A041476, A040238.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 18 2013