A041173 Denominators of continued fraction convergents to sqrt(96).
1, 1, 4, 5, 94, 99, 391, 490, 9211, 9701, 38314, 48015, 902584, 950599, 3754381, 4704980, 88444021, 93149001, 367891024, 461040025, 8666611474, 9127651499, 36049565971, 45177217470, 849239480431, 894416697901, 3532489574134, 4426906272035, 83216802470764
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,98,0,0,0,-1).
Crossrefs
Cf. A041172.
Programs
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Magma
I:=[1, 1, 4, 5, 94, 99, 391, 490]; [n le 8 select I[n] else 98*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
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Mathematica
Denominator[Convergents[Sqrt[96],201]] (* or *) CoefficientList[Series[(1 + x + 4 x^2 + 5 x^3 - 4 x^4 + x^5 - x^6)/(1 - 98 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
Formula
G.f.: (1 +x +4*x^2 +5*x^3 -4*x^4 +x^5 -x^6)/(1 -98*x^4 +x^8). - Vincenzo Librandi, Dec 12 2013
a(n) = 98*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 12 2013
Extensions
More terms from Vincenzo Librandi, Dec 12 2013