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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: A141240 A298892 A038318 * A097531 A131029 A033331

Adjacent sequences:  A010183 A010184 A010185 * A010187 A010188 A010189

KEYWORD

nonn,cofr,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 9 03:27 EST 2019. Contains 329872 sequences. (Running on oeis4.)