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A042785 Denominators of continued fraction convergents to sqrt(923). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 24 16:26 EDT 2019. Contains 322430 sequences. (Running on oeis4.)