A112971 Row sums of the matrix ((1,xc(x))^2 mod 2), where c(x) is the g.f. of A000108.

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, 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, 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

Offset: 0

Author

Paul Barry, Oct 07 2005

Keywords

• easy
• nonn

Comments

(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.

Crossrefs

Cf. A112970.

Formula

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)}