The On-Line Encyclopedia of Integer Sequences (OEIS)

A042107 revision #16

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

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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