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A041147 Denominators of continued fraction convergents to sqrt(83). 2
1, 9, 163, 1476, 26731, 242055, 4383721, 39695544, 718903513, 6509827161, 117895792411, 1067571958860, 19334191051891, 175075291425879, 3170689436717713, 28711280221885296, 519973733430653041, 4708474881097762665, 85272521593190381011, 772161169219811191764 (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 (0,164,0,-1).

FORMULA

G.f.: -(x^2-9*x-1) / (x^4-164*x^2+1). - Colin Barker, Nov 13 2013

a(n) = 164*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013

MATHEMATICA

Denominator/@Convergents[Sqrt[83], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)

CoefficientList[Series[(1 + 9 x - x^2)/(x^4 - 164 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)

LinearRecurrence[{0, 164, 0, -1}, {1, 9, 163, 1476}, 30] (* Harvey P. Dale, Nov 09 2017 *)

PROG

(MAGMA) I:=[1, 9, 163, 1476]; [n le 4 select I[n] else 164*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013

CROSSREFS

Cf. A041146, A040073, A020840, A010534.

Sequence in context: A157574 A077280 A297436 * A041144 A212334 A086759

Adjacent sequences:  A041144 A041145 A041146 * A041148 A041149 A041150

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)