A041147 Denominators of continued fraction convergents to sqrt(83).

1, 9, 163, 1476, 26731, 242055, 4383721, 39695544, 718903513, 6509827161, 117895792411, 1067571958860, 19334191051891, 175075291425879, 3170689436717713, 28711280221885296, 519973733430653041, 4708474881097762665, 85272521593190381011, 772161169219811191764

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 A354900

Adjacent sequences: A041144 A041145 A041146 * A041148 A041149 A041150

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Status

approved