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A041026 Numerators of continued fraction convergents to sqrt(18). 2
4, 17, 140, 577, 4756, 19601, 161564, 665857, 5488420, 22619537, 186444716, 768398401, 6333631924, 26102926097, 215157040700, 886731088897, 7309005751876, 30122754096401, 248291038523084 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
G.f.: (4+17*x+4*x^2-x^3)/(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) = ((-4-3*sqrt(2))/(17+12*sqrt(2))^n+(-4+3*sqrt(2))*(17+12*sqrt(2))^n)/2.
a1(n) = (1/(17+12*sqrt(2))^n+(17+12*sqrt(2))^n)/2. (End)
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[18], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
Numerator[Convergents[Sqrt[18], 20]] (* or *) LinearRecurrence[{0, 34, 0, -1}, {4, 17, 140, 577}, 20] (* Harvey P. Dale, Jun 12 2014 *)
a0[n_] := ((-4-3*Sqrt[2])/(17+12*Sqrt[2])^n+(-4+3*Sqrt[2])*(17+12*Sqrt[2])^n)/2 // Simplify
a1[n_] := (1/(17+12*Sqrt[2])^n+(17+12*Sqrt[2])^n)/2 // Simplify
Flatten[MapIndexed[{a0[#], a1[#]} &, Range[20]]] (* Gerry Martens, Jul 11 2015 *)
CROSSREFS
Sequence in context: A032335 A208803 A156076 * A072755 A320444 A129436
KEYWORD
nonn,cofr,frac,easy
AUTHOR
STATUS
approved

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Last modified July 20 15:17 EDT 2024. Contains 374459 sequences. (Running on oeis4.)