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
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
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Jan 26 2008
STATUS
approved