A131711 Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1.
0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1, 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,1,0,-1,0,1,0,-1,0,1).
Programs
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Mathematica
PadRight[{},120,{0,1,2,5,2,9,0,9,8,5,8,1}] (* Harvey P. Dale, Dec 29 2014 *)
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PARI
[0,1,2,5,2,9,0,9,8,5,8,1][n%12+1] \\ Charles R Greathouse IV, Jun 02 2011
Formula
G.f.: (x^8+8x^7+4x^6+5x^4+4x^2+2x+1)x/((1-x) (1+x) (x^2+x+1) (x^2-x+1) (x^4-x^2+1)). a(n) = |A131201(n)| = A000129(n) mod 10 = A000129(n)-10*A131727(n). [From R. J. Mathar, Sep 20 2008]
a(n) = 25/6 -4*cos(Pi*n/6)/sqrt(3) -sqrt(3)*sin(Pi*n/6) -5*cos(Pi*n/3)/3 -5*cos(2*Pi*n/3)/3 +4*cos(5*Pi*n/6)/sqrt(3) +sqrt(3)*sin(5*Pi*n/6) -5*(-1)^n/6. - R. J. Mathar, Oct 08 2011
Comments