A042151 Denominators of continued fraction convergents to sqrt(600).

1, 2, 97, 196, 9505, 19206, 931393, 1881992, 91267009, 184416010, 8943235489, 18070886988, 876345810913, 1770762508814, 85872946233985, 173516654976784, 8414672385119617, 17002861425216018, 824552020795488481, 1666106903016192980, 80797683365572751521

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,98,0,-1).

Crossrefs

Cf. A042150, A040575.

Programs

Magma

I:=[1,2,97,196]; [n le 4 select I[n] else 98*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[600], 30]] (* Vincenzo Librandi, Jan 15 2014 *)
LinearRecurrence[{0,98,0,-1},{1,2,97,196},30] (* Harvey P. Dale, Jul 04 2022 *)

Formula

G.f.: -(x^2-2*x-1) / ((x^2-10*x+1)*(x^2+10*x+1)). - Colin Barker, Dec 02 2013

a(n) = 98*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 15 2014

Extensions

More terms from Colin Barker, Dec 02 2013