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%I #5 Apr 27 2023 09:11:32
%S 1,2,6,16,62,192,652,2048,9270,31744,116948,393216,1533868,5341184,
%T 19445016,67108864,332958758,1215037440,4711687300,16642998272,
%U 67697833092,245257732096,923984441000,3298534883328,13952454631996
%N Coefficients of the solution to a functional equation.
%C G.f. A(x) satisfies A(4*x^2) = A(x) + A(-x) = -4*A(x)*A(-x). Also A(4*x^2) = 4 * A(x)^2/(1 + 4*A(x)).
%o (PARI) a(n)=local(A,m); if(n<1,0,A=x+O(x^2); m=1; while(m<=n,m*=2; A=subst(A,x,x^2); A=A/2+sqrt(A^2/4+A)); polcoeff(A,n)*4^(n-1))
%K nonn
%O 1,2
%A _Michael Somos_, Mar 20 2004