A041930 - OEIS

%I #16 Sep 08 2022 08:44:55

%S 22,243,10714,118097,5206982,57394899,2530582538,27893802817,

%T 1229857906486,13556330774163,597708411969658,6588348862440401,

%U 290485058359347302,3201923990815260723,141175140654230819114

%N Numerators of continued fraction convergents to sqrt(488).

%H Vincenzo Librandi, <a href="/A041930/b041930.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 (0,486,0,-1).

%F G.f.: (22 + 243*x + 22*x^2 - x^3)/(1 - 486*x^2 + x^4). - _Vincenzo Librandi_, Nov 12 2013

%F a(n) = 486*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 12 2013

%t Numerator[Convergents[Sqrt[488], 30]] (* or *) CoefficientList[Series[(22 + 243 x + 22 x^2 - x^3)/(1 - 486 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 12 2013 *)

%o (Magma) I:=[22,243,10714,118097]; [n le 4 select I[n] else 486*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 12 2013

%Y Cf. A041931.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.