login
A216178
Period 4: repeat [4, 1, 0, -3].
1
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
0,1
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)
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 *)
PROG
(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
(PARI) a(n)=[4, 1, 0, -3][n%4+1] \\ Charles R Greathouse IV, Jul 17 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Brad Clardy, Mar 10 2013
STATUS
approved