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

0,5

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.

Links

Table of n, a(n) for n=0..99.

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)}

Crossrefs

Cf. A112970.

Sequence in context: A129138 A353378 A112970 * A299201 A342085 A050379

Adjacent sequences: A112968 A112969 A112970 * A112972 A112973 A112974

Keyword

easy,nonn

Author

Paul Barry, Oct 07 2005

Status

approved