%I A110161
%S A110161 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 A110161 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 A110161 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 A110161 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 A110161 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 A110161 -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 A110161 Expansion of x(1-x^2)/(1-x^2+x^4).
%C A110161 Transform of A002605 by the Riordan array A102587. Denominator is the 
               12th cyclotomic polynomial.
%F A110161 Periodic of length 12: 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1 - T. D. Noe 
               (noe(AT)sspectra.com), Dec 12 2006
%F A110161 a(n)=(1/12)*{[n mod 12]-[(n+1) mod 12]-[(n+4) mod 12]+[(n+5) mod 12]-[(n+6) 
               mod 12]+[(n+7) mod 12]+[(n+10) mod 12]-[(n+11) mod 12]}, with n>=0. 
               - Paolo P. Lava (ppl(AT)spl.at), Jun 01 2007
%F A110161 Euler transform of length 12 sequence [ 0, 0, 0, -1, 0, -1, 0, 0, 0, 
               0, 0, 1]. - Michael Somos Jun 11 2007
%F A110161 a(n) is multiplicative with a(2^e) = a(3^e) = 0^e, a(p^e) = 1 if p == 
               1, 11 (mod 12), a(p^e) = (-1)^e if p == 5, 7 (mod 12). - Michael 
               Somos Jun 11 2007
%F A110161 G.f.: x *(1-x^4) *(1-x^6)/ (1-x^12). a(n) = a(-n) = -a(n+6). - Michael 
               Somos Jun 11 2007
%o A110161 (PARI) {a(n)= kronecker(12,n)} /* Michael Somos Jun 11 2007 */
%Y A110161 Sequence in context: A122415 A071038 A109017 this_sequence A134667 A117943 
               A096268
%Y A110161 Adjacent sequences: A110158 A110159 A110160 this_sequence A110162 A110163 
               A110164
%K A110161 easy,sign,mult
%O A110161 0,1
%A A110161 Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
%E A110161 Corrected by T. D. Noe (noe(AT)sspectra.com), Dec 12 2006