A115382 Correlation triangle for Thue-Morse sequence A010060(n+1).

1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 3, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 3, 1, 0, 2, 0, 0, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 0, 2, 1, 1, 3, 1, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 4, 1, 1, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1

Offset: 0

Author

Paul Barry, Jan 21 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A115383. T(2n,n) gives A115384(n+1).

Examples

			Triangle begins
1,
1, 1,
0, 2, 0,
1, 1, 1, 1,
0, 1, 2, 1, 0,
0, 1, 1, 1, 1, 0,
1, 0, 1, 3, 1, 0, 1,
1, 1, 1, 1, 1, 1, 1, 1,
0, 2, 0, 1, 3, 1, 0, 2, 0,
0, 1, 1, 2, 1, 1, 2, 1, 1, 0,
1, 0, 2, 1, 1, 3, 1, 1, 2, 0, 1,
0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 0,
1, 1, 0, 2, 1, 1, 4, 1, 1, 2, 0, 1, 1,
1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 1,
0, 2, 1, 0, 2, 1, 1, 5, 1, 1, 2, 0, 1, 2, 0,
1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1,
0, 1, 2, 2, 0, 2, 2, 1, 5, 1, 2, 2, 0, 2, 2, 1, 0
		

Formula

G.f.: A(x)A(x*y)/(1-x^2*y) where A(x) is the g.f. of A010060(n+1). Number triangle T(n, k)=sum{j=0..n, if(j<=k, A010060(k-j+1), 0)*if(j<=(n-k), A010060(n-k-j+1), 0)}.