A134668 Period 6: repeat [1, -1, 0, 0, -1, 1].

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

Offset

0,1

Comments

The Fi2 sums, see A180662, of triangle A108299 equal the terms of this sequence. - Johannes W. Meijer, Aug 11 2011

Links

Table of n, a(n) for n=0..77.

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

Formula

First differences of A134667.

Euler transform of length 6 sequence [-1, 0, 0, -1, 0, 1]. - Michael Somos, Feb 08 2008

a(n) = a(-1-n) for all n in Z. - Michael Somos, Feb 08 2008

G.f.: (1-x)*(1-x^4) / (1-x^6) = (1-x)*(1+x^2) / ((1-x+x^2)*(1+x+x^2)) = (1-x+x^2-x^3) / (1+x^2+x^4).

a(6*n + 2) = a(6*n + 3) = 0. - Michael Somos, Oct 16 2015

From Wesley Ivan Hurt, Jun 20 2016: (Start)

a(n) + a(n-2) + a(n-4) = 0 for n>3.

a(n) = cos(n*Pi/6) * (3*cos(n*Pi/2) + 2*sqrt(3)*sin(n*Pi/6) - 3*sqrt(3)*sin(n*Pi/2))/3. (End)

Example

G.f. = 1 - x - x^4 + x^5 + x^6 - x^7 - x^10 + x^11 + x^12 - x^13 - x^16 + ...

Maple

A134668 :=proc(n): (1/6)*(-2*((n+1) mod 6)+((n+2) mod 6)-((n+4) mod 6)+2*((n+5) mod 6)) end: seq(A134668(n), n=0..74); # Johannes W. Meijer, Aug 14 2011

Mathematica

PadRight[{}, 120, {1, -1, 0, 0, -1, 1}] (* or *) LinearRecurrence[{0, -1, 0, -1}, {1, -1, 0, 0}, 120] (* Harvey P. Dale, Dec 03 2012 *)

Prog

(PARI) {a(n)=[1, -1, 0, 0, -1, 1][n%6+1]}; /* Michael Somos, Feb 08 2008 */
(Magma) &cat [[1, -1, 0, 0, -1, 1]^^20]; // Wesley Ivan Hurt, Jun 20 2016

Crossrefs

Cf. A108299, A134667, A180662.

Sequence in context: A359374 A188192 A068432 * A309970 A039963 A267537

Adjacent sequences: A134665 A134666 A134667 * A134669 A134670 A134671

Keyword

sign,easy

Author

Paul Curtz, Jan 26 2008

Status

approved