A042099 Denominators of continued fraction convergents to sqrt(573).

1, 1, 15, 16, 751, 767, 11489, 12256, 575265, 587521, 8800559, 9388080, 440652239, 450040319, 6741216705, 7191257024, 337539039809, 344730296833, 5163763195471, 5508493492304, 258554463841455, 264062957333759, 3955435866514081, 4219498823847840

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 766, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+16*x^2+1) / (x^8-766*x^4+1). - Colin Barker, Dec 01 2013

a(n) = 766*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[573], 30]] (* Vincenzo Librandi, Jan 14 2014 *)

Prog

(Magma) I:=[1, 1, 15, 16, 751, 767, 11489, 12256]; [n le 8 select I[n] else 766*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Jan 14 2014

Crossrefs

Cf. A042098, A040549.

Sequence in context: A041476 A041477 A041478 * A156530 A077033 A043669

Adjacent sequences: A042096 A042097 A042098 * A042100 A042101 A042102

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 01 2013

Status

approved