A041962 - OEIS

%I #17 Sep 08 2022 08:44:55

%S 22,45,202,449,19958,40365,181418,403201,17922262,36247725,162913162,

%T 362074049,16094171318,32550416685,146295838058,325142092801,

%U 14452547921302,29230237935405,131373499662922

%N Numerators of continued fraction convergents to sqrt(504).

%H Vincenzo Librandi, <a href="/A041962/b041962.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 (0,0,0,898,0,0,0,-1).

%F G.f.: -(x^7-22*x^6+45*x^5-202*x^4-449*x^3-202*x^2-45*x-22)/(x^8-898*x^4+1). - _Vincenzo Librandi_, Nov 12 2013

%F a(n) = 898*a(n-4)-a(n-8). - _Vincenzo Librandi_, Nov 12 2013

%t Numerator[Convergents[Sqrt[504], 30]] (* or *) CoefficientList[Series[-(x^7 - 22 x^6 + 45 x^5 - 202 x^4 - 449 x^3 - 202 x^2 - 45 x - 22)/(x^8 - 898 x^4 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 12 2013 *)

%o (Magma) I:=[22,45,202,449,19958,40365,181418,403201]; [n le 8 select I[n] else 898*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 12 2013

%Y Cf. A041963.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.