A041872 - OEIS

%I #14 Jun 13 2015 00:49:37

%S 21,43,107,4537,9181,22899,970939,1964777,4900493,207785483,420471459,

%T 1048728401,44467064301,89982857003,224432778307,9516159545897,

%U 19256751870101,48029663286099,2036502609886259

%N Numerators of continued fraction convergents to sqrt(458).

%H Vincenzo Librandi, <a href="/A041872/b041872.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,214,0,0,1).

%F G.f.: (21 + 43*x + 107*x^2 + 43*x^3 - 21*x^4 + x^5)/(1 - 214*x^3 - x^6). [_Bruno Berselli_, Nov 11 2013]

%F a(n) = 214*a(n-3) + a(n-6) for n>5. [_Bruno Berselli_, Nov 11 2013]

%t Numerator[Convergents[Sqrt[458], 20]] (* _Harvey P. Dale_, Aug 26 2013 *)

%t LinearRecurrence[{0, 0, 214, 0, 0, 1}, {21, 43, 107, 4537, 9181, 22899}, 30] (* _Bruno Berselli_, Nov 11 2013 *)

%Y Cf. A041873.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.