%I A093114
%S A093114 1,2,2,16,14,64,484,2048,3798,7168,96292,131072,1247476,3964928,
%T A093114 27170632,67108864,220816742,497811456,993377620,3758096384,38457826404,
%U A093114 201938960384,1217833409416,1099511627776,4275253627140
%V A093114 1,-2,-2,-16,14,64,-484,-2048,3798,-7168,96292,131072,-1247476,3964928,
               -27170632,
%W A093114 -67108864,220816742,-497811456,993377620,-3758096384,38457826404,-201938960384,
%X A093114 1217833409416,1099511627776,-4275253627140
%N A093114 Coefficients of the solution to a functional equation.
%C A093114 G.f. A(x) satisfies A(-4x^2)=A(x)+A(-x), A(4x^2)=-4A(x)A(-x).
%F A093114 a(n)*(-4)^n = 2*a(2n) - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 04 
               2004
%F A093114 Given g.f. A(x), then B(x)=4A(x/4) satisfies 0=f(B(x), B(x^2), B(x^4)) 
               where f(u, v, w)=u^2v+uw-v^2.
%F A093114 Given g.f. A(x), then B(x)=4A(x/4) satisfies B(-x^2)=B(x)+B(-x) and B(x^2)=-B(x)*B(-x).
%o A093114 (PARI) a(n)=local(A,A2,m); if(n<1,0,A=x+O(x^2); m=1; while(m<=n,m*=2; 
               A2=subst(A,x,-x^2); A=A2/2+sqrt(A2^2/4+subst(A,x,x^2))); polcoeff(A,
               n)*4^(n-1))
%Y A093114 Sequence in context: A097540 A112327 A152541 this_sequence A016740 A133922 
               A088139
%Y A093114 Adjacent sequences: A093111 A093112 A093113 this_sequence A093115 A093116 
               A093117
%K A093114 sign
%O A093114 1,2
%A A093114 Michael Somos, Mar 20 2004