A144534 Denominators of continued fraction convergents to sqrt(8/9).
1, 1, 17, 35, 577, 1189, 19601, 40391, 665857, 1372105, 22619537, 46611179, 768398401, 1583407981, 26102926097, 53789260175, 886731088897, 1827251437969, 30122754096401, 62072759630771, 1023286908188737, 2108646576008245, 34761632124320657, 71631910824649559
Offset: 0
Examples
0, 1, 16/17, 33/35, 544/577, 1121/1189, 18480/19601, 38081/40391, 627776/665857, ...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,34,0,-1).
Programs
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Magma
I:=[1,1,17,35]; [n le 4 select I[n] else 34*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 01 2014
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[8/9], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *) Denominator[Convergents [Sqrt[8/9], 30]] (* Vincenzo Librandi, Feb 01 2014 *)
Formula
a(n) = 16*a(n-1) + a(n-2) if n odd, otherwise a(n) = 2*a(n-1) + a(n-2), for n >= 2.
a(n) = 34*a(n-2)-a(n-4). G.f.: (x^3-17*x^2+x+1)/((x^2-6*x+1)*(x^2+6*x+1)). [Colin Barker, Jul 16 2012]
Comments