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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
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
FORMULA
a(n) = 3 - 2 * 0^(n mod 4).
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
KEYWORD
frac,nonn,easy
AUTHOR
Reinhard Zumkeller, Nov 13 2009
EXTENSIONS
Definition corrected by D. S. McNeil, May 09 2010
STATUS
approved