The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..100 Index entries for linear recurrences with constant coefficients, signature (0,34,0,-1). 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 Cf. A010474, A041026. Sequence in context: A297515 A027169 A152041 * A362820 A364946 A209034 Adjacent sequences: A041024 A041025 A041026 * A041028 A041029 A041030 KEYWORD nonn,cofr,frac,easy AUTHOR N. J. A. Sloane STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 30 05:35 EDT 2023. Contains 365781 sequences. (Running on oeis4.)