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A167817 Period 4: repeat [1, 3, 3, 3]. 3
1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1, 3, 3, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Denominator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/3; numerator = A167816(n).

Continued fraction expansion of (33 + sqrt(2805))/66. - Klaus Brockhaus, May 06 2010

LINKS

Table of n, a(n) for n=0..104.

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

FORMULA

a(n) = 3 - 2 * 0^(n mod 4).

a(n) = (1/12)*{11*(n mod 4) + 5*[(n+1) mod 4] + 5*[(n+2) mod 4] - [(n+3) mod 4]}. - Paolo P. Lava, Nov 17 2009

a(n) = (1/2)*(5 - I^n - (-1)^n - (-I)^n). - Paolo P. Lava, May 04 2010

G.f.: (1 + 3*x + 3*x^2 + 3*x^3)/(1-x^4). - Klaus Brockhaus, May 06 2010

a(n) = 5/2 - cos(Pi*n/2) - (-1)^n/2. - R. J. Mathar, Oct 08 2011

E.g.f.: -cos(x) + 3*sinh(x) + 2*cosh(x). - Ilya Gutkovskiy, Jun 27 2016

a(n) = a(n-4) for n>3. - Wesley Ivan Hurt, Jul 09 2016

MAPLE

seq(op([1, 3, 3, 3]), n=0..50); # Wesley Ivan Hurt, Jul 09 2016

MATHEMATICA

Denominator[LinearRecurrence[{1, 1}, {0, 1/3}, 110]] (* or *) PadRight[{}, 110, {1, 3, 3, 3}] (* Harvey P. Dale, Dec 07 2014 *)

LinearRecurrence[{0, 0, 0, 1}, {1, 3, 3, 3}, 105] (* Ray Chandler, Aug 03 2015 *)

PROG

(MAGMA) &cat[[1, 3, 3, 3]: n in [0..50]]; // Vincenzo Librandi, Dec 28 2010

CROSSREFS

Cf. A130196.

Cf. A177344 (decimal expansion of (33+sqrt(2805))/66). - Klaus Brockhaus, May 06 2010

Sequence in context: A323596 A323375 A140366 * A153401 A181520 A256736

Adjacent sequences:  A167814 A167815 A167816 * A167818 A167819 A167820

KEYWORD

frac,nonn,easy

AUTHOR

Reinhard Zumkeller, Nov 13 2009

EXTENSIONS

Definition corrected by D. S. McNeil, May 09 2010

STATUS

approved

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Last modified August 3 05:55 EDT 2020. Contains 336197 sequences. (Running on oeis4.)