%I A134667
%S A134667 0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,
%T A134667 1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,
%U A134667 0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0
%V A134667 0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,
               0,0,0,-1,0,1,0,0,
%W A134667 0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,
               0,1,0,0,0,-1,0,
%X A134667 1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0,0,0,-1,0,1,0
%N A134667 Period 6: repeat 0, 1, 0, 0, 0, -1.
%F A134667 a(n)=(1/6)*{-(n mod 6)+[(n+1) mod 6]+[(n+4) mod 6]-[(n+5) mod 6]}, with 
               n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jan 28 2008
%F A134667 Euler transform of length 6 sequence [ 0, 0, 0, -1, 0, 1]. - Michael 
               Somos Feb 10 2008
%F A134667 G.f.: x * (1 - x^4) / (1 - x^6) = (x + x^3) / (1 + x^2 + x^4).
%F A134667 G.f. A(x) satisfies 0 = f(A(x), A(x^2), A(x^3)) where f(u, v, w) = w 
               * (2 + v - u^2 - 2*v^2) - 2 * u * v. - Michael Somos Aug 11 2009
%F A134667 a(n) is multiplicative with a(p^e) = 0^e if p = 2 or p = 3, a(p^e) = 
               1 if p == 1 (mod 6), a(p^e) = (-1)^e if p == 5 (mod 6). - Michael 
               Somos Aug 11 2009
%F A134667 a(-n) = -a(n). a(n+6) = a(n). a(2*n) = a(3*n) = 0.
%e A134667 x - x^5 + x^7 - x^11 + x^13 - x^17 + x^19 - x^23 + x^25 - x^29 + ...
%o A134667 (PARI) {a(n) = [0, 1, 0, 0, 0, -1][n%6+1]} /* Michael Somos Feb 10 2008 
               */
%o A134667 (PARI) {a(n) = kronecker(-12, n)} /* Michael Somos Feb 10 2008 */
%o A134667 (PARI) {a(n) = if( n < 0, -a(-n), if( n<1, 0, direuler(p=2, n, 1 / (1 
               - kronecker(-12, p) * X))[n]))} /* Michael Somos Aug 11 2009 */
%Y A134667 Cf. A120325, A131719, A131720, A131735, A131736.
%Y A134667 Sequence in context: A071038 A109017 A110161 this_sequence A117943 A096268 
               A079101
%Y A134667 Adjacent sequences: A134664 A134665 A134666 this_sequence A134668 A134669 
               A134670
%K A134667 sign,easy,mult
%O A134667 0,1
%A A134667 Paul Curtz (bpcrtz(AT)free.fr), Jan 26 2008