A042533 - OEIS

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

%S 1,5,46,235,13206,66265,609591,3114220,175005911,878143775,8078299886,

%T 41269643205,2319178319366,11637161240035,107053629479681,

%U 546905308638440,30733750913232321,154215659874800045,1418674689786432726,7247589108806963675

%N Denominators of continued fraction convergents to sqrt(795).

%H Vincenzo Librandi, <a href="/A042533/b042533.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 13252, 0, 0, 0, -1).

%F G.f.: -(x^2 -5*x -1)*(x^4 +47*x^2 +1) / (x^8 -13252*x^4 +1). - _Colin Barker_, Dec 17 2013

%F a(n) = 13252*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Jan 23 2014

%t Denominator[Convergents[Sqrt[795], 30]] (* _Harvey P. Dale_, Nov 12 2011 *)

%t CoefficientList[Series[-(x^2 - 5 x - 1) (x^4 + 47 x^2 + 1)/(x^8 - 13252 x^4 + 1), {x, 0, 25}], x] (* _Vincenzo Librandi_, Jan 23 2014 *)

%o (Magma) I:=[1,5,46,235,13206,66265,609591,3114220]; [n le 8 select I[n] else 13252*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Jan 23 2014

%Y Cf. A042532, A040766.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E Additional term from _Colin Barker_, Dec 17 2013