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A042325
Denominators of continued fraction convergents to sqrt(689).
2
1, 4, 209, 840, 43889, 176396, 9216481, 37042320, 1935417121, 7778710804, 406428378929, 1633492226520, 85348024157969, 343025588858396, 17922678644794561, 72033740168036640, 3763677167382699841, 15126742409698836004, 790354282471722172049
OFFSET
0,2
FORMULA
G.f.: -(x^2-4*x-1) / (x^4-210*x^2+1). - Colin Barker, Dec 07 2013
a(n) = 210*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 20 2014
MATHEMATICA
Denominator[Convergents[Sqrt[689], 30]] (* Vincenzo Librandi, Jan 20 2014 *)
LinearRecurrence[{0, 210, 0, -1}, {1, 4, 209, 840}, 20] (* Harvey P. Dale, Sep 26 2023 *)
PROG
(Magma) I:=[1, 4, 209, 840]; [n le 4 select I[n] else 210*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 20 2014
CROSSREFS
Sequence in context: A293159 A340176 A038790 * A091287 A338282 A281997
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Dec 07 2013
STATUS
approved