A152892 Period 5: repeat [0, 3, 1, 0, 1].
0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1, 0, 3, 1, 0, 1
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).
Programs
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Maple
seq((n^3+2*n^2)mod 5,n=0..50); # Gary Detlefs, Mar 20 2010
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Mathematica
PadRight[{},120,{0,3,1,0,1}] (* Harvey P. Dale, Oct 04 2016 *)
Formula
a(n+5) = a(n) with a(0) = a(3) = 0, a(1) = 3 and a(2) = a(4) = 1.
O.g.f: ((3*z+z^2+z^4)/(1-z^5)).
a(n) = 1 + (-1/2 + (3/10)*sqrt(5))*cos(2*n*Pi/5) + ((1/5)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/10)*sqrt(2)*sqrt(5 - sqrt(5)))*sin(2*n*Pi/5) + (-1/2 - (3/10)*sqrt(5))*cos(4*n*Pi/5) + (-(1/10)*sqrt(2)*sqrt(5 + sqrt(5)) + (1/5)*sqrt(2)*sqrt(5-sqrt(5)))*sin(4*n*Pi/5).
a(n) = (n^3 + 2*n^2) mod 5. - Gary Detlefs, Mar 20 2010