A041967 Denominators of continued fraction convergents to sqrt(506).

1, 2, 89, 180, 8009, 16198, 720721, 1457640, 64856881, 131171402, 5836398569, 11803968540, 525211014329, 1062225997198, 47263154891041, 95588535779280, 4253158729179361, 8601905994138002, 382737022471251449, 774075950936640900, 34442078863683451049

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, 90, 0, -1).

Formula

G.f.: -(x^2 -2*x -1) / (x^4 -90*x^2 +1). - Colin Barker, Nov 28 2013

a(n) = 90*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 28 2013

Mathematica

Denominator[Convergents[Sqrt[506], 30]] (* Vincenzo Librandi, Dec 28 2013 *)
LinearRecurrence[{0, 90, 0, -1}, {1, 2, 89, 180}, 40] (* Harvey P. Dale, Jan 21 2016 *)

Prog

(Magma) I:=[1, 2, 89, 180]; [n le 4 select I[n] else 90*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 28 2013

Crossrefs

Cf. A041966, A040483.

Sequence in context: A235467 A249305 A023302 * A226768 A246871 A024239

Adjacent sequences: A041964 A041965 A041966 * A041968 A041969 A041970

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved