A041945 - OEIS

%I #21 Sep 08 2022 08:44:55

%S 1,4,177,712,31505,126732,5607713,22557584,998141409,4015123220,

%T 177663563089,714669375576,31623116088433,127207133729308,

%U 5628737000177985,22642155134441248,1001883562915592897,4030176406796812836,178329645461975357681,717348758254698243560

%N Denominators of continued fraction convergents to sqrt(495).

%H Vincenzo Librandi, <a href="/A041945/b041945.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 (0,178,0,-1).

%F G.f.: -(x^2-4*x-1) / (x^4-178*x^2+1). - _Colin Barker_, Nov 27 2013

%F a(n) = 178*a(n-2) - a(n-4) for n>3. - _Vincenzo Librandi_, Dec 27 2013

%t Denominator[Convergents[Sqrt[495], 30]] (* _Harvey P. Dale_, Aug 22 2013 *)

%t CoefficientList[Series[(1 + 4 x - x^2)/(x^4 - 178 x^2 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 27 2013 *)

%t LinearRecurrence[{0,178,0,-1},{1,4,177,712},20] (* _Harvey P. Dale_, Aug 13 2021 *)

%o (Magma) I:=[1,4,177,712]; [n le 4 select I[n] else 178*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 27 2013

%Y Cf. A041944, A040472.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 27 2013