A114116 1's-counting matrix: row sums give number of 1's in binary expansion of n+1.

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

Offset: 0

Author

Paul Barry, Nov 13 2005

Keywords

• sign
• tabl

Comments

First column is -A037861(n+1). Row sums are A000120. Product of partial sum matrix (1/(1-x),x) and A114115. Inverse is A114117.

Examples

			Triangle begins
1;
0, 1;
2,-1, 1;
-1, 2,-1, 1;
1, 0, 1,-1, 1;
1, 0, 0, 1,-1, 1;
3,-2, 2,-1, 1,-1, 1;