A152893 Periodic sequence [3, 3, 0, 0, 4] of period 5.

3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4, 3, 3, 0, 0, 4

Offset: 0

Author

Richard Choulet, Dec 14 2008

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1).

Crossrefs

Cf. A026056.

Programs

Mathematica

PadRight[{},120,{3,3,0,0,4}] (* Harvey P. Dale, Sep 17 2018 *)

Formula

a(n+5) = a(n) with a(0) = a(1) = 3, a(2) = a(3) = 0 and a(4) = 4.

O.g.f: ((3+3*z+4*z^4)/(1-z^5)).

a(n) = 2+(1/2+7/10*5^(1/2))*cos(2*n*Pi/5)+(-1/10*2^(1/2)*(5+5^(1/2))^(1/2))*sin(2*n*Pi/5)+(1/2-7/10*5^(1/2))*cos(4*n*Pi/5)+(-1/10*2^(1/2)*(5-5^(1/2))^(1/2))*sin(4*n*Pi/5).

a(n) = [(n-2)^3 -(n-2)^2] mod 5. [Gary Detlefs, Mar 20 2010]