A041161 Denominators of continued fraction convergents to sqrt(90).
1, 2, 37, 76, 1405, 2886, 53353, 109592, 2026009, 4161610, 76934989, 158031588, 2921503573, 6001038734, 110940200785, 227881440304, 4212806126257, 8653493692818, 159975692596981, 328604878886780
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).
Crossrefs
Cf. A041160.
Programs
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Magma
I:=[1, 2, 37, 76]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 12 2013
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Mathematica
Denominator[Convergents[Sqrt[90],30]] (* Harvey P. Dale, May 20 2013 *) CoefficientList[Series[(1 + 2 x - x^2)/(x^4 - 38 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
Formula
G.f.: (1 +2*x -x^2)/(x^4 -38*x^2 +1). - Vincenzo Librandi, Dec 12 2013
a(n) = 38*a(n-2) - a(n-4), - Vincenzo Librandi, Dec 12 2013