A042009 Denominators of continued fraction convergents to sqrt(527).

1, 1, 22, 23, 1034, 1057, 23231, 24288, 1091903, 1116191, 24531914, 25648105, 1153048534, 1178696639, 25905677953, 27084374592, 1217618160001, 1244702534593, 27356371386454, 28601073921047, 1285803623912522, 1314404697833569, 28888302278417471

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, 1056, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+23*x^2+1) / (x^8-1056*x^4+1). - Colin Barker, Nov 28 2013

a(n) = 1056*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 12 2014

Mathematica

Denominator[Convergents[Sqrt[527], 40]] (* Vincenzo Librandi, Jan 12 2014 *)

Prog

(Magma) I:=[1, 1, 22, 23, 1034, 1057, 23231, 24288]; [n le 8 select I[n] else 1056*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Jan 12 2014

Crossrefs

Cf. A042008, A040504.

Sequence in context: A042004 A042006 A042008 * A042010 A162334 A165483

Adjacent sequences: A042006 A042007 A042008 * A042010 A042011 A042012

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 28 2013

Status

approved