%I A099493
%S A099493 1,0,1,2,1,0,3,4,3,8,7,10,23,8,33,56,1,104,121,58,297,232,291,780,349,
               1072,
%T A099493 1903,174,3407,4272,1505,9840,8543,8752,26321,13902,33777,65456,11805,
               110356,
%U A099493 150173,35192,325303,310054,257319,885496,537919,1054888,2240927
%V A099493 1,0,1,2,-1,0,3,-4,-3,8,-7,-10,23,-8,-33,56,1,-104,121,58,-297,232,291,
               -780,349,1072,
%W A099493 -1903,174,3407,-4272,-1505,9840,-8543,-8752,26321,-13902,-33777,65456,
               -11805,-110356,
%X A099493 150173,35192,-325303,310054,257319,-885496,537919,1054888,-2240927
%N A099493 Expansion of (1+x^2)^2/(1+x^2-2x^3+x^4+x^6).
%C A099493 A Chebyshev transform of A052907, which has g.f. 1/(1-2x^2-2x^3). The 
               image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
%F A099493 a(n)=-a(n-2)+2a(n-3)-a(n-4)-a(n-6); a(n)=sum{k=0..floor(n/2), C(n-k, 
               k)(-1)^k*sum{j=0.., floor(n-2k/2), C(j, n-2k-2j)2^j}}.
%Y A099493 Sequence in context: A106378 A094301 A135488 this_sequence A088523 A145460 
               A035543
%Y A099493 Adjacent sequences: A099490 A099491 A099492 this_sequence A099494 A099495 
               A099496
%K A099493 easy,sign
%O A099493 0,4
%A A099493 Paul Barry (pbarry(AT)wit.ie), Oct 19 2004