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

0,2

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A042126, A040563.

Sequence in context: A203516 A159783 A028370 * A219163 A017546 A144044

Adjacent sequences: A042124 A042125 A042126 * A042128 A042129 A042130

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved