A041189 Denominators of continued fraction convergents to sqrt(105).
1, 4, 81, 328, 6641, 26892, 544481, 2204816, 44640801, 180768020, 3660001201, 14820772824, 300075457681, 1215122603548, 24602527528641, 99625232718112, 2017107181890881, 8168053960281636, 165378186387523601, 669680799510376040
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,82,0,-1).
Programs
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Magma
I:=[1,4,81,328]; [n le 4 select I[n] else 82*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013
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Mathematica
Denominator/@Convergents[Sqrt[105],30] (* Harvey P. Dale, Apr 02 2011 *) CoefficientList[Series[(1 + 4 x - x^2)/(1 - 82 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013*)
Formula
G.f.: (1 + 4*x - x^2)/(1 - 82*x^2 + x^4). - Vincenzo Librandi, Dec 12 2013
a(n) = 82*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 12 2013
Extensions
a(19) from Vincenzo Librandi, Dec 12 2013
Comments