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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A010186 Continued fraction for sqrt(125). 5
11, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5, 22, 5, 1, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Periodic with period [5,1,1,5,22] of length 5 (after the initial term). - M. F. Hasler, Sep 09 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

G. Xiao, 'Contfrac' tool on WIMS.

Index entries for continued fractions for constants

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

FORMULA

a(n) = (1/25)*(-68*(n mod 5)-3*((n+1) mod 5)+17*((n+2) mod 5)+37*((n+3) mod 5)+102*((n+4) mod 5))-11*(C(2*n,n) mod 2). - Paolo P. Lava, Jul 24 2009

G.f.: (11+5*x+x^2+x^3+5*x^4+11*x^5)/((1-x)*(1+x+x^2+x^3+x^4)). - Bruno Berselli, Sep 10 2011

MATHEMATICA

ContinuedFraction[Sqrt[125], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2011*)

LinearRecurrence[{0, 0, 0, 0, 1}, {11, 5, 1, 1, 5, 22}, 80] (* or *) PadRight[ {11}, 80, {22, 5, 1, 1, 5}] (* Harvey P. Dale, Oct 05 2016 *)

PROG

(PARI) default(realprecision, 199); contfrac(sqrt(125))  \\ _M. F. Hasler, Sep 09 2011

(PARI) a(n)=[22, 5, 1, 1, 5][n%5+1]-11*!n  \\ M. F. Hasler, Sep 09 2011

CROSSREFS

Cf. A172074.

Sequence in context: A166205 A141240 A038318 * A097531 A131029 A033331

Adjacent sequences:  A010183 A010184 A010185 * A010187 A010188 A010189

KEYWORD

nonn,cofr,easy,nice

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 5 21:40 EST 2016. Contains 278771 sequences.