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A041055
Denominators of continued fraction convergents to sqrt(33).
2
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
0,3
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]
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 *)
CROSSREFS
Sequence in context: A172144 A032837 A127614 * A246626 A032838 A013336
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved