A042785 Denominators of continued fraction convergents to sqrt(923).

1, 2, 3, 5, 8, 21, 1268, 2557, 3825, 6382, 10207, 26796, 1617967, 3262730, 4880697, 8143427, 13024124, 34191675, 2064524624, 4163240923, 6227765547, 10391006470, 16618772017, 43628550504, 2634331802257, 5312292155018, 7946623957275, 13258916112293

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, 1276, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10-2*x^9+3*x^8-5*x^7+8*x^6-21*x^5-8*x^4-5*x^3-3*x^2-2*x-1) / (x^12-1276*x^6+1). - Colin Barker, Dec 23 2013

a(n) = 1276*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 23 2013

Maple

convert(sqrt(923), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[923], 30]] (* Wesley Ivan Hurt, Dec 23 2013 *)
CoefficientList[Series[-(x^10 - 2 * x^9 + 3 * x^8 - 5 * x^7 + 8 * x^6 - 21 * x^5 - 8 * x^4 - 5 * x^3 - 3 * x^2 - 2 * x - 1)/(x^12 - 1276 * x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 23 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 1276, 0, 0, 0, 0, 0, -1}, {1, 2, 3, 5, 8, 21, 1268, 2557, 3825, 6382, 10207, 26796}, 30] (* Harvey P. Dale, Jul 04 2017 *)

Prog

(Magma) I:=[1, 2, 3, 5, 8, 21, 1268, 2557, 3825, 6382, 10207, 26796]; [n le 12 select I[n] else 1276*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A042784, A040892.

Sequence in context: A053056 A041157 A178356 * A136682 A107467 A191425

Adjacent sequences: A042782 A042783 A042784 * A042786 A042787 A042788

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 23 2013

Status

approved