A041087 Denominators of continued fraction convergents to sqrt(51).
1, 7, 99, 700, 9899, 69993, 989801, 6998600, 98970201, 699790007, 9896030299, 69972002100, 989504059699, 6996500419993, 98940509939601, 699580069997200, 9893061489900401, 69951010499300007, 989207208480100499, 6994401469860003500, 98910827786520149499
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,100,0,-1).
Programs
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Magma
I:=[1, 7, 99, 700]; [n le 4 select I[n] else 100*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[51], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *) CoefficientList[Series[(1 + 7 x - x^2)/(x^4 - 100 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
Formula
G.f.: -(x^2-7*x-1) / (x^4-100*x^2+1). - Colin Barker, Nov 12 2013
a(n) = 100*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 11 2013
Extensions
More terms from Colin Barker, Nov 12 2013