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

0,1

Links

Table of n, a(n) for n=0..49.

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

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) = (1/5)*{2*(n mod 5)-3*[(n+1) mod 5]+[(n+2) mod 5]+4*[(n+3) mod 5]+[(n+4) mod 5]}, with n>=0. [Paolo P. Lava, Dec 15 2008]

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

Mathematica

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

Crossrefs

Cf. A026056.

Sequence in context: A170852 A245320 A330341 * A335682 A335681 A297978

Adjacent sequences: A152890 A152891 A152892 * A152894 A152895 A152896

Keyword

easy,nonn

Author

Richard Choulet, Dec 14 2008

Status

approved