OFFSET
1,2
COMMENTS
G.f. A(x) satisfies A(-4x^2)=A(x)+A(-x), A(4x^2)=-4A(x)A(-x).
FORMULA
a(n)*(-4)^n = 2*a(2n) - Paul D. Hanna, Apr 04 2004
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.
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).
PROG
(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))
CROSSREFS
KEYWORD
sign
AUTHOR
Michael Somos, Mar 20 2004
STATUS
approved