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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
OFFSET
0,2
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
KEYWORD
nonn,frac,easy
AUTHOR
STATUS
approved