A041055 Denominators of continued fraction convergents to sqrt(33).
1, 1, 3, 4, 43, 47, 137, 184, 1977, 2161, 6299, 8460, 90899, 99359, 289617, 388976, 4179377, 4568353, 13316083, 17884436, 192160443, 210044879, 612250201, 822295080, 8835201001, 9657496081, 28150193163
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,46,0,0,0,-1).
Programs
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[33], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *) Denominator[Convergents[Sqrt[33], 30]] (* Vincenzo Librandi, Oct 23 2013 *) LinearRecurrence[{0,0,0,46,0,0,0,-1},{1,1,3,4,43,47,137,184},30] (* Harvey P. Dale, Apr 24 2022 *)
Formula
a(n) = 46*a(n-4)-a(n-8). G.f.: -(x^2-x-1)*(x^4+4*x^2+1)/(x^8-46*x^4+1). [Colin Barker, Jul 16 2012]