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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041034 Numerators of continued fraction convergents to sqrt(22). 3
4, 5, 14, 61, 136, 197, 1712, 1909, 5530, 24029, 53588, 77617, 674524, 752141, 2178806, 9467365, 21113536, 30580901, 265760744, 296341645, 858444034, 3730117781, 8318679596, 12048797377, 104709058612 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
FORMULA
a(n) = 394*a(n-6)-a(n-12). G.f.: -(x^11 -4*x^10 +5*x^9 -14*x^8 +61*x^7 -136*x^6 -197*x^5 -136*x^4 -61*x^3 -14*x^2 -5*x -4)/(x^12-394*x^6+1). [Colin Barker, Jul 16 2012]
MATHEMATICA
Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[22], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
CoefficientList[Series[- (x^11 - 4 x^10 + 5 x^9 - 14 x^8 + 61 x^7 - 136 x^6 - 197 x^5 - 136 x^4 - 61 x^3 - 14 x^2 - 5 x - 4)/(x^12 - 394 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 394, 0, 0, 0, 0, 0, -1}, {4, 5, 14, 61, 136, 197, 1712, 1909, 5530, 24029, 53588, 77617}, 30] (* Harvey P. Dale, Mar 14 2017 *)
CROSSREFS
Sequence in context: A352683 A182252 A041857 * A281911 A042535 A222489
KEYWORD
nonn,cofr,frac,easy
AUTHOR
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 20 18:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)