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URL: https://oeis.org/A041115

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A041115
Denominators of continued fraction convergents to sqrt(66).
3
1, 8, 129, 1040, 16769, 135192, 2179841, 17573920, 283362561, 2284474408, 36834953089, 296964099120, 4788260539009, 38603048411192, 622437035118081, 5018099329355840, 80912026304811521, 652314309767848008, 10517940982590379649
OFFSET
0,2
FORMULA
a(n) = 16*a(n-1) + a(n-2) for n >= 2 even and a(n) = 8*a(n-1) + a(n-2) for n >= 2 odd. - Nathaniel Johnston, Jun 26 2011
From Colin Barker, Feb 28 2013: (Start)
a(n) = 130*a(n-2) - a(n-4).
G.f.: -(x^2 - 8*x - 1) / (x^4 - 130*x^2 + 1). (End)
a(2n) = A041495(2n), a(2n+1) = A041495(2n+1)*2. - M. F. Hasler, Feb 23 2020
MAPLE
a := proc(n) option remember: if(n<=1)then return (n+1)^3: fi: if(n mod 2 = 0)then return 16*a(n-1) + a(n-2): else return 8*a(n-1) + a(n-2): fi: end: seq(a(n), n=0..20); # Nathaniel Johnston, Jun 26 2011
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[66], n]]], {n, 1, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)
CoefficientList[Series[(1 + 8 x - x^2)/(x^4 - 130 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 11 2013 *)
PROG
(Magma) I:=[1, 8, 129, 1040]; [n le 4 select I[n] else 130*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 11 2013
CROSSREFS
Sequence in context: A104997 A265097 A027951 * A348546 A041112 A348207
KEYWORD
nonn,frac,easy
STATUS
approved