A216178 Period 4: repeat [4, 1, 0, -3].

4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3, 4, 1, 0, -3

Offset: 0

Author

Brad Clardy, Mar 10 2013

Keywords

• sign
• easy

Links

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

Crossrefs

Cf. A084100, A168361, A214864.

Programs

Magma

for n in [0 .. 50] do (3*(-1)^n+1)/2 + 2*(-1)^((2*n-1+(-1)^n)/4); end for;

Magma

&cat [[4, 1, 0, -3]^^30]; // Wesley Ivan Hurt, Jul 09 2016

Maple

seq(op([4, 1, 0, -3]), n=0..40); # Wesley Ivan Hurt, Jul 09 2016

Mathematica

PadRight[{},100,{4,1,0,-3}] (* or *) LinearRecurrence[{0,0,0,1},{4,1,0,-3},100] (* Harvey P. Dale, Nov 28 2014 *)

PARI

a(n)=[4, 1, 0, -3][n%4+1] \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = (3*(-1)^n+1)/2 + 2*(-1)^((2*n-1+(-1)^n)/4).

a(n) = A168361(n+1) + A084100(n+4).

G.f.: (4+x-3*x^3) / ((1-x)*(1+x)*(1+x^2)). - R. J. Mathar, Mar 10 2013

a(n+4) = a(n). - Alexander R. Povolotsky, Mar 15 2013

From Wesley Ivan Hurt, Jul 09 2016: (Start)

a(n) = 1/2+3*I^(2*n)/2+(1+I)*I^(-n)+(1-I)*I^n.

a(n) = (1+3*cos(n*Pi)+4*cos(n*Pi/2)+4*sin(n*Pi/2)+3*I*sin(n*Pi))/2. (End)