A042677 Denominators of continued fraction convergents to sqrt(868).

1, 2, 13, 249, 511, 9958, 60259, 130476, 7627867, 15386210, 99945127, 1914343623, 3928632373, 76558358710, 463278784633, 1003115927976, 58644002607241, 118291121142458, 768390729461989, 14717714980920249, 30203820691302487, 588590308115667502

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, 7688126, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^14 -2*x^13 +13*x^12 -249*x^11 +511*x^10 -9958*x^9 +60259*x^8 -130476*x^7 -60259*x^6 -9958*x^5 -511*x^4 -249*x^3 -13*x^2 -2*x -1) / (x^16 -7688126*x^8 +1). - Colin Barker, Dec 20 2013

a(n) = 7688126*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[868], 30]] (* Harvey P. Dale, Sep 24 2013 *)
CoefficientList[Series[-(x^14 - 2 x^13 + 13 x^12 - 249 x^11 + 511 x^10 - 9958 x^9 + 60259 x^8 - 130476 x^7 - 60259 x^6 - 9958 x^5 - 511 x^4 - 249 x^3 - 13 x^2 - 2 x - 1)/(x^16 - 7688126 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 2, 13, 249, 511, 9958, 60259, 130476, 7627867, 15386210, 99945127, 1914343623, 3928632373, 76558358710, 463278784633, 1003115927976]; [n le 16 select I[n] else 7688126*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A042676, A040838.

Sequence in context: A135870 A133067 A276744 * A338424 A134296 A086510

Adjacent sequences: A042674 A042675 A042676 * A042678 A042679 A042680

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 20 2013

Status

approved