A152894 Periodic sequence [0,0,1,4,0] of period 5.
0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0, 1, 4, 0, 0, 0
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).
Crossrefs
Cf. A026062.
Programs
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Maple
seq((n^3-n) mod 5,n=0..50); # Gary Detlefs, Mar 20 2010
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Mathematica
PadRight[{},90,{0,0,1,4,0}] (* Harvey P. Dale, Jan 29 2013 *)
Formula
a(n+5) = a(n) with a(0) = a(1) = a(4) = 0, a(2) = 1 and a(3) = 4;
O.g.f.: (z^2+4*z^3)/(1-z^5);
a(n) = 1 + (-1/2 - (1/2)*sqrt(5))*cos(2*n*Pi/5) + (-(3/10)*sqrt(2)*sqrt(5 - sqrt(5)))*sin(2*n*Pi/5) + (-1/2 + (1/2)*sqrt(5))*cos(4*n*Pi/5) + ((3/10)*sqrt(2)*sqrt(5 + sqrt(5)))*sin(4*n*Pi/5).
a(n) = (n^3 - n) mod 5. - Gary Detlefs, Mar 20 2010