A042127 Denominators of continued fraction convergents to sqrt(588).

1, 4, 193, 776, 37441, 150540, 7263361, 29203984, 1409054593, 5665422356, 273349327681, 1099062733080, 53028360515521, 213212504795164, 10287228590683393, 41362126867528736, 1995669318232062721, 8024039399795779620, 387149560508429484481

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 (0,194,0,-1).

Crossrefs

Cf. A042126, A040563.

Programs

Magma

I:=[1,4,193,776]; [n le 4 select I[n] else 194*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[588], 30]] (* Vincenzo Librandi, Jan 15 2014 *)
LinearRecurrence[{0,194,0,-1},{1,4,193,776},20] (* Harvey P. Dale, Dec 05 2018 *)

Formula

G.f.: -(x^2-4*x-1) / ((x^2-14*x+1)*(x^2+14*x+1)). - Colin Barker, Dec 02 2013

a(n) = 194*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 15 2014

Extensions

More terms from Colin Barker, Dec 02 2013