%I A099494
%S A099494 1,0,1,1,1,0,0,2,0,1,1,1,2,1,0,1,2,1,1,1,0,2,0,0,1,1,1,0,1,0,1,0,1,1,1,
%T A099494 0,0,2,0,1,1,1,2,1,0,1,2,1,1,1,0,2,0,0,1,1,1,0,1,0,1,0,1,1,1,0,0,2,0,1,
%U A099494 1,1,2,1,0,1,2,1,1,1,0,2,0,0,1,1,1
%V A099494 1,0,1,1,-1,0,0,-2,0,1,-1,1,2,-1,0,1,-2,-1,1,-1,0,2,0,0,1,-1,-1,0,-1,0,
               1,0,1,1,-1,0,0,
%W A099494 -2,0,1,-1,1,2,-1,0,1,-2,-1,1,-1,0,2,0,0,1,-1,-1,0,-1,0,1,0,1,1,-1,0,0,
               -2,0,1,-1,1,2,
%X A099494 -1,0,1,-2,-1,1,-1,0,2,0,0,1,-1,-1
%N A099494 A Chebyshev transform of Fib(n)+(-1)^n.
%C A099494 A Chebyshev transform of A008346, which has g.f. 1/(1-2x^2-x^3). The 
               image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
%F A099494 G.f.: (1+x^2)^2/(1+x^2-x^3+x^4+x^6); a(n)=-a(n-2)+a(n-3)-a(n-4)-a(n-6); 
               a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k(F(n-2k)+(-1)^(n-2k)}; 
               a(n)=A014019(n-1)+A000484(n).
%Y A099494 Sequence in context: A029425 A025902 A053692 this_sequence A030341 A121444 
               A118230
%Y A099494 Adjacent sequences: A099491 A099492 A099493 this_sequence A099495 A099496 
               A099497
%K A099494 easy,sign
%O A099494 0,8
%A A099494 Paul Barry (pbarry(AT)wit.ie), Oct 19 2004