A042139 Denominators of continued fraction convergents to sqrt(594).

1, 2, 3, 8, 43, 1040, 5243, 11526, 16769, 45064, 2179841, 4404746, 6584587, 17573920, 94454187, 2284474408, 11516826227, 25318126862, 36834953089, 98988033040, 4788260539009, 9675509111058, 14463769650067, 38603048411192, 207479011706027, 5018099329355840

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,2196610,0,0,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^18 -2*x^17 +3*x^16 -8*x^15 +43*x^14 -1040*x^13 +5243*x^12 -11526*x^11 +16769*x^10 -45064*x^9 -16769*x^8 -11526*x^7 -5243*x^6 -1040*x^5 -43*x^4 -8*x^3 -3*x^2 -2*x -1) / (x^20 -2196610*x^10 +1). - Colin Barker, Dec 02 2013

a(n) = 2196610*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[594], 30]] (* Vincenzo Librandi, Jan 15 2014 *)

Crossrefs

Cf. A042138, A040569.

Sequence in context: A064794 A127005 A042553 * A118127 A100644 A013208

Adjacent sequences: A042136 A042137 A042138 * A042140 A042141 A042142

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved