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A041029
Denominators of continued fraction convergents to sqrt(19).
3
1, 2, 3, 11, 14, 39, 326, 691, 1017, 3742, 4759, 13260, 110839, 234938, 345777, 1272269, 1618046, 4508361, 37684934, 79878229, 117563163, 432567718, 550130881, 1532829480, 12812766721, 27158362922
OFFSET
0,2
LINKS
FORMULA
a(n) = 340*a(n-6)-a(n-12). G.f.: -(x^10- 2*x^9+ 3*x^8 -11*x^7 +14*x^6 -39*x^5 -14*x^4 -11*x^3 -3*x^2 -2*x -1)/(x^12-340*x^6+1). [Colin Barker, Jul 16 2012]
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[19], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 11 x^7 + 14 x^6 - 39 x^5 - 14 x^4 - 11 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 340 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
CROSSREFS
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved