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%I #3 Mar 30 2012 18:59:12
%S 1,1,1,1,2,1,2,1,3,2,2,1,4,2,2,1,6,3,4,2,4,2,2,1,8,4,4,2,4,2,2,1,11,6,
%T 6,3,8,4,4,2,8,4,4,2,4,2,2,1,16,8,8,4,8,4,4,2,8,4,4,2,4,2,2,1,22,11,
%U 12,6,12,6,6,3,16,8,8,4,8,4,4,2,16,8,8,4,8,4,4,2,8,4,4,2,4,2,2,1,32,16,16,8
%N Row sums of the matrix ((1,xc(x))^2 mod 2), where c(x) is the g.f. of A000108.
%C (1,xc(x)) is the Riordan array T(n,k)=[x^n](xc(x))^k. Conjectures: a(2^n)=a(2^(n+1)+1)=A005578(n);a(2^n-1)=a(3*2^n-1)=1.
%F a(n)=sum{k=0..n, mod(sum{i=0..n, sum{j=0..n, ((2j+1)/(n+j+1))(-1)^(j-i)C(2n, n+j)C(j, i)}* sum{l=0..i, ((2l+1)/(i+l+1))(-1)^(l-k)C(2i, i+l)C(l, k)}}, 2)}
%Y Cf. A112970.
%K easy,nonn
%O 0,5
%A _Paul Barry_, Oct 07 2005
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