A042735 - OEIS

%I #19 Sep 08 2022 08:44:55

%S 1,1,19,20,1179,1199,22761,23960,1412441,1436401,27267659,28704060,

%T 1692103139,1720807199,32666632721,34387439920,2027138148081,

%U 2061525588001,39134598732099,41196124320100,2428509809297899,2469705933617999,46883216614421881

%N Denominators of continued fraction convergents to sqrt(897).

%H Vincenzo Librandi, <a href="/A042735/b042735.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, 1198, 0, 0, 0, -1).

%F G.f.: -(x^2-x-1)*(x^4+20*x^2+1) / (x^8-1198*x^4+1). - _Colin Barker_, Dec 22 2013

%F a(n) = 1198*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Jan 27 2014

%t Denominator[Convergents[Sqrt[897], 30]] (* _Harvey P. Dale_, May 29 2013 *)

%o (Magma) I:=[1,1,19,20,1179,1199,22761,23960]; [n le 8 select I[n] else 1198*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Jan 27 2014

%Y Cf. A042734, A040867.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 22 2013