A042598 - OEIS

%I #18 Sep 08 2022 08:44:55

%S 28,29,115,259,892,1151,65348,66499,264845,596189,2053412,2649601,

%T 150431068,153080669,609673075,1372426819,4726953532,6099380351,

%U 346292253188,352391633539,1403467153805,3159325941149

%N Numerators of continued fraction convergents to sqrt(828).

%H Vincenzo Librandi, <a href="/A042598/b042598.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 2302, 0, 0, 0, 0, 0, -1).

%F G.f.: (28 +29*x +115*x^2 +259*x^3 +892*x^4 +1151*x^5 +892*x^6 -259*x^7 +115*x^8 -29*x^9 +28*x^10 -x^11)/(1 -2302*x^6 +x^12). - _Vincenzo Librandi_, Nov 29 2013

%F a(n) = 2302*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 29 2013

%t Numerator[Convergents[Sqrt[828], 30]] (* or *) CoefficientList[Series[(28 + 29 x + 115 x^2 + 259 x^3 + 892 x^4 + 1151 x^5 + 892 x^6 - 259 x^7 + 115 x^8 - 29 x^9 + 28 x^10 - x^11)/(1 - 2302 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 29 2013 *)

%o (Magma) I:=[28, 29, 115, 259, 892, 1151, 65348, 66499, 264845, 596189, 2053412, 2649601]; [n le 12 select I[n] else 2302*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 29 2013

%Y Cf. A042599.

%K nonn,frac,easy

%O 0,1

%A _N. J. A. Sloane_.