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A041027
Denominators of continued fraction convergents to sqrt(18).
5
1, 4, 33, 136, 1121, 4620, 38081, 156944, 1293633, 5331476, 43945441, 181113240, 1492851361, 6152518684, 50713000833, 209004522016, 1722749176961, 7100001229860, 58522759015841, 241191037293224
OFFSET
0,2
FORMULA
G.f.: (1+4*x-x^2)/(1-34*x^2+x^4). - Colin Barker, Jan 02 2012
From Gerry Martens, Jul 11 2015: (Start)
Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
a0(n) = ((3+2*sqrt(2))/(17+12*sqrt(2))^n+(3-2*sqrt(2))*(17+12*sqrt(2))^n)/6.
a1(n) = (-1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/(6*sqrt(2)). (End)
MATHEMATICA
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[18], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
a0[n_] := ((3+2*Sqrt[2])/(17+12*Sqrt[2])^n+(3-2*Sqrt[2])*(17+12*Sqrt[2])^n)/6 // Simplify
a1[n_] := (-1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/(6*Sqrt[2]) // Simplify
Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)
LinearRecurrence[{0, 34, 0, -1}, {1, 4, 33, 136}, 20] (* Harvey P. Dale, Jan 05 2019 *)
CROSSREFS
Sequence in context: A297515 A027169 A152041 * A362820 A364946 A209034
KEYWORD
nonn,cofr,frac,easy
STATUS
approved