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A130196
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Period 3: repeat [1, 2, 2].
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24
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1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2
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OFFSET
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0,2
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COMMENTS
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From Reinhard Zumkeller, Nov 12 2009: (Start)
Denominator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/2; numerator = A167808;
a(n) = A131534(n) + A022003(n) = A080425(n) - A131534(n) + 2 = A153727(n)/A131534(n). (End)
Continued fraction expansion of (5+sqrt(85))/10. - Klaus Brockhaus, May 07 2010
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LINKS
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Table of n, a(n) for n=0..104.
Index entries for linear recurrences with constant coefficients, signature (0,0,1).
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FORMULA
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a(n+3) = a(n) with a(0)=1, a(1)=a(2)=2.
a(n) = (1/9)*(8*(n mod 3) + 5*((n+1) mod 3) + 2*((n+2) mod 3)). - Paolo P. Lava, Aug 28 2007
G.f.: (1+2*x+2*x^2)/(1-x)*(x^2+x+1). - R. J. Mathar, Nov 14 2007
a(n) = 5/3 + (2/3)*(-1/2 - (1/2)*i*sqrt(3))^(-2)*(-1/2 - (1/2)*i*sqrt(3))^n + (2/3)*(-1/2 + (1/2)*i*sqrt(3))^(-2)*(-1/2 + (1/2)*i*sqrt(3))^n + (1/3)*(-1/2 - (1/2)*i*sqrt(3))^n + (1/3)*(-1/2 + (1/2)*i*sqrt(3))^n + (2/3)*(-1/2 - (1/2)*i*sqrt(3))^(-1)*(-1/2 - (1/2)*i*sqrt(3))^n + (2/3)*(-1/2 + (1/2)*i*sqrt(3))^(-1)*(-1/2 + (1/2)*i*sqrt(3))^n, with i=sqrt(-1). - Paolo P. Lava, Jul 17 2008
a(n) = (5 - 2*cos(2*Pi*n/3))/3. - Jaume Oliver Lafont, Nov 23 2008
a(n) = 2 - 0^(n mod 3). - Reinhard Zumkeller, Nov 12 2009
a(n) = A011655(n) + 1 = (n^2 mod 3) + 1. - Boris Putievskiy, Feb 03 2013
a(n) = floor((n+1)*5/3) - floor(n*5/3). - Hailey R. Olafson, Jul 23 2014
E.g.f.: (5*exp(x) - 2*exp(-x/2)*cos(sqrt(3)*x/2))/3. - Stefano Spezia, Jun 03 2021
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MAPLE
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A130196:=n->floor(5*(n+1)/3)-floor(5*n/3): seq(A130196(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2014
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MATHEMATICA
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Table[Floor[5 (n + 1)/3] - Floor[5 n/3], {n, 0, 100}] (* Wesley Ivan Hurt, Jul 24 2014 *)
Denominator[LinearRecurrence[{1, 1}, {0, 1/2}, 110]] (* or *) PadRight[{}, 110, {1, 2, 2}] (* Harvey P. Dale, Aug 08 2014 *)
LinearRecurrence[{0, 0, 1}, {1, 2, 2}, 105] (* Ray Chandler, Aug 03 2015 *)
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PROG
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(PARI) a(n)=2-0^(n%3) \\ Charles R Greathouse IV, Jun 01 2011
(Magma) [Floor(5*(n+1)/3)-Floor(5*n/3) : n in [0..100]]; // Wesley Ivan Hurt, Jul 24 2014
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CROSSREFS
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Cf. A177347 (decimal expansion of (5+sqrt(85))/10).
Cf. A022003, A080425, A131534, A153727, A167808.
Sequence in context: A098398 A306211 A131714 * A230866 A158209 A234538
Adjacent sequences: A130193 A130194 A130195 * A130197 A130198 A130199
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Aug 05 2007
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EXTENSIONS
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More terms from Klaus Brockhaus, May 07 2010
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STATUS
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approved
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