A152856 Periodic sequence [4,0,4,3,4] of period 5.
4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4, 4, 0, 4, 3, 4
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).
Crossrefs
Programs
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Mathematica
PadRight[{},100,{4,0,4,3,4}] (* Harvey P. Dale, Jun 08 2014 *)
Formula
a(n+5) = a(n) with a(0) = a(2) = a(4) = 4, a(1) = 0 and a(3) = 3
a(n) = 3+(1/2-3/10*5^(1/2))*cos(2*n*Pi/5)+(-1/10*(4*(5+5^(1/2))^(1/2)-(5-5^(1/2))^(1/2))*2^(1/2))*sin(2*n*Pi/5)+(3/10*5^(1/2)+1/2)*cos(4*n*Pi/5)+(-1/10*((5+5^(1/2))^(1/2)+4*(5-5^(1/2))^(1/2))*2^(1/2))*sin(4*n*Pi/5)
o.g.f f(z) = (4+4*z^2+3*z^3+4*z^4)/(1-z^5)