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A110627 Bisection of A083952 such that the self-convolution is congruent modulo 4 to A083952, which consists entirely of 1's and 2's.

%I A110627 #4 Mar 30 2012 18:36:49
%S A110627 1,1,2,1,2,1,1,2,2,2,2,2,2,1,2,1,1,2,1,2,2,2,2,2,2,1,1,2,1,2,1,1,2,2,
%T A110627 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,1,1,2,
%U A110627 1,2,2,2,2,2,2,1,1,2,2,2,1,2,1,1,2,1,1,1,1,2,1,2,1,2,2,2,1,1,2,1,1,1,2,2,2
%N A110627 Bisection of A083952 such that the self-convolution is congruent modulo 4 to A083952, which consists entirely of 1's and 2's.
%C A110627 Congruent modulo 2 to A084202 and A108336; the self-convolution of A084202 equals A083952.
%F A110627 a(n) = A083952(2*n) for n>=0. G.f. satisfies: A(x^2) = G(x) - 2*x/(1-x^2), where G(x) is the g.f. of A083952. G.f. satisfies: A(x)^2 = A(x^2) + 2*x/(1-x^2) + 4*x^2*H(x) where H(x) is the g.f. of A111581.
%o A110627 (PARI) {a(n)=local(p=2,A,C,X=x+x*O(x^(p*n)));if(n==0,1, A=sum(i=0,n-1,a(i)*x^(p*i))+p*x*((1-x^(p-1))/(1-X))/(1-X^p); for(k=1,p,C=polcoeff((A+k*x^(p*n))^(1/p),p*n); if(denominator(C)==1,return(k);break)))}
%Y A110627 Cf. A083952, A111581, A084202, A108336.
%K A110627 nonn
%O A110627 0,3
%A A110627 _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 08 2005