A041155 Denominators of continued fraction convergents to sqrt(87).
1, 3, 55, 168, 3079, 9405, 172369, 526512, 9649585, 29475267, 540204391, 1650088440, 30241796311, 92375477373, 1693000389025, 5171376644448, 94777779989089, 289504716611715, 5305862678999959, 16207092753611592, 297033532244008615, 907307689485637437
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,56,0,-1).
Crossrefs
Cf. A041154.
Programs
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Magma
I:=[1, 3, 55, 168]; [n le 4 select I[n] else 56*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
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Mathematica
Denominator/@Convergents[Sqrt[87], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *) CoefficientList[Series[(1 + 3 x - x^2)/(x^4 - 56 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
Formula
G.f.: (1 +3*x -x^2)/(x^4 -56*x^2 +1), - Vincenzo Librandi, Dec 12 2013
a(n) = 56*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 12 2013