A042107 Denominators of continued fraction convergents to sqrt(578).

1, 24, 1153, 27696, 1330561, 31961160, 1535466241, 36883150944, 1771926711553, 42563124228216, 2044801889665921, 49117808476210320, 2359699608747761281, 56681908418422481064, 2723091303693026852353, 65410873197051066937536, 3142445004762144239854081

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1154,0,-1).

Formula

G.f.: -(x^2-24*x-1) / ((x^2-34*x+1)*(x^2+34*x+1)). - Colin Barker, Dec 01 2013

a(n) = 1154*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[578], 30]] (* Vincenzo Librandi, Jan 14 2014 *)

Prog

(Magma) I:=[1, 24, 1153, 27696]; [n le 4 select I[n] else 1154*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 14 2014

Crossrefs

Cf. A042106, A040553.

Sequence in context: A323994 A090675 A144618 * A042104 A069991 A035025

Adjacent sequences: A042104 A042105 A042106 * A042108 A042109 A042110

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 01 2013

Status

approved