A130196 Period 3: repeat [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, 1, 2, 2
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,1).
Crossrefs
Programs
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Magma
[Floor(5*(n+1)/3)-Floor(5*n/3) : n in [0..100]]; // Wesley Ivan Hurt, Jul 24 2014
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Maple
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
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 *) -
PARI
a(n)=2-0^(n%3) \\ Charles R Greathouse IV, Jun 01 2011
Formula
a(n+3) = a(n) with a(0)=1, a(1)=a(2)=2.
G.f.: (1+2*x+2*x^2)/(1-x)*(x^2+x+1). - R. J. Mathar, Nov 14 2007
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
Extensions
More terms from Klaus Brockhaus, May 07 2010
Comments