A131379 Period 4: repeat [1, 0, -1, 1].

1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1, 1, 0, -1, 1

Offset

0,1

Links

Table of n, a(n) for n=0..79.

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

Formula

a(n) = 1/4 + cos(1/2*Pi*n) - 1/2*sin(1/2*Pi*n) + 1/4*(-1)^(1+n). - R. J. Mathar, Nov 15 2007

G.f.: (1-x^2+x^3) / ((1-x)*(1+x)*(x^2+1)). - R. J. Mathar, Jun 02 2011

a(n) = a(n-4) for n>3. - Wesley Ivan Hurt, Jul 09 2016

a(n) = 1 - A130731(n+3). - Wesley Ivan Hurt, Dec 23 2016

Maple

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

Mathematica

PadRight[{}, 100, {1, 0, -1, 1}] (* Wesley Ivan Hurt, Jul 09 2016 *)
CoefficientList[Series[(1 - x^2 + x^3)/((1 - x) (1 + x) (x^2 + 1)), {x, 0, 80}], x] (* Michael De Vlieger, Dec 23 2016 *)

Prog

(Magma) &cat [[1, 0, -1, 1]^^30]; // Wesley Ivan Hurt, Jul 09 2016

Crossrefs

Cf. A130731.

Sequence in context: A104521 A317198 A354993 * A359819 A284677 A191232

Adjacent sequences: A131376 A131377 A131378 * A131380 A131381 A131382

Keyword

sign,easy

Author

Paul Curtz, Oct 01 2007

Status

approved