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%I #3 Apr 30 2014 01:38:50
%S 1,1,1,0,1,1,1,-1,0,1,2,1,0,0,0,0,0,-1,-1,1,4,3,1,-2,1,1,0,-3,-3,1,4,
%T 4,-1,-3,-3,2,0,-4,-4,1,11,9,3,-6,-1,3,3,-8,-10,2,13,14,-3,-10,-7,4,0,
%U -12,-15,1,25,21,3,-16,-5,7,3,-18,-26,1,29,34,-5,-24,-17,11,5,-27,-36,0,58,54,12,-37,-12,20,15,-42,-63,-1
%N Expansion of solution to a functional equation.
%F Given g.f. A(x), then B(x)=x*A(x^5) satisfies 0=f(B(x),B(x^2),B(x^4)) where f(u,v,w)=uv^4+v^3w^2+u^2w^3-u^3vw.
%o (PARI) a(n)=local(B,A,k); if(n<0,0, k=(3+sqrtint(9+40*n))\10; A= sum(i=-k,k,(-1)^i*x^((5*i^2+3*i)/2), x*O(x^n)) /sum(i=-k,k,(-1)^i*x^((5*i^2+i)/2), x*O(x^n)); B=k=1; while(k<=n,k*=2; B/=A; A=subst(A,x,x^2) +x*O(x^n)); polcoeff(B,n))
%o (PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1,n, (1-x^k)^-sum(i=0,valuation(k,2),kronecker(5,k/2^i)), 1+x*O(x^n)), n))}
%Y Cf. A007325.
%K sign
%O 0,11
%A _Michael Somos_, Dec 01 2004