login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041115 Denominators of continued fraction convergents to sqrt(66). 2
1, 8, 129, 1040, 16769, 135192, 2179841, 17573920, 283362561, 2284474408, 36834953089, 296964099120, 4788260539009, 38603048411192, 622437035118081, 5018099329355840, 80912026304811521, 652314309767848008, 10517940982590379649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..250

Index entries for linear recurrences with constant coefficients, signature (0,130,0,-1).

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)

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

Cf. A041114.

Sequence in context: A104997 A265097 A027951 * A041112 A073701 A239756

Adjacent sequences:  A041112 A041113 A041114 * A041116 A041117 A041118

KEYWORD

nonn,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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 01:41 EST 2019. Contains 329242 sequences. (Running on oeis4.)