A042274 - OEIS

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

%S 25,26,77,103,5227,5330,15887,21217,1076737,1097954,3272645,4370599,

%T 221802595,226173194,674148983,900322177,45690257833,46590580010,

%U 138871417853,185461997863,9411971311003,9597433308866

%N Numerators of continued fraction convergents to sqrt(663).

%H Vincenzo Librandi, <a href="/A042274/b042274.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, 206, 0, 0, 0, -1).

%F G.f.: (25 +26*x +77*x^2 +103*x^3 +77*x^4 -26*x^5 +25*x^6 -x^7)/(1 -206*x^4 +x^8). - _Vincenzo Librandi_, Nov 20 2013

%F a(n) = 206*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 18 2013

%t Numerator[Convergents[Sqrt[663], 30]] (* _Harvey P. Dale_, Aug 21 2011 *)

%t CoefficientList[Series[(25 + 26 x + 77 x^2 + 103 x^3 + 77 x^4 - 26 x^5 + 25 x^6 - x^7)/(1 - 206 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 20 2013 *)

%o (Magma) I:=[25, 26, 77, 103, 5227, 5330, 15887, 21217]; [n le 8 select I[n] else 206*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013

%Y Cf. A042275.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.