A042081 Denominators of continued fraction convergents to sqrt(564).

1, 1, 3, 4, 187, 191, 569, 760, 35529, 36289, 108107, 144396, 6750323, 6894719, 20539761, 27434480, 1282525841, 1309960321, 3902446483, 5212406804, 243673159467, 248885566271, 741444292009, 990329858280, 46296617772889, 47286947631169

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,190,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-190*x^4+1). - Colin Barker, Dec 01 2013

a(n) = 190*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[564], 30]] (* Harvey P. Dale, Nov 08 2011 *)
CoefficientList[Series[(1 + x - x^2) (x^4 + 4 x^2 + 1)/(x^8 - 190 x^4 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 14 2014 *)

Prog

(Magma) I:=[1, 1, 3, 4, 187, 191, 569, 760]; [n le 8 select I[n] else 190*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Jan 14 2014

Crossrefs

Cf. A042080, A040540.

Sequence in context: A156513 A082213 A097172 * A245456 A042275 A012861

Adjacent sequences: A042078 A042079 A042080 * A042082 A042083 A042084

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 01 2013

Status

approved