A155040 A symmetric (1,-1)-triangle.

1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1

Offset: 0

Author

Paul Barry, Jan 19 2009

Keywords

• easy
• sign
• tabl

Comments

Row sums are A007877(n+1). Diagonal sums are A155041.

Examples

			Triangle begins
.1,
.1, 1,
.1, -1, 1,
.1, -1, -1, 1,
.1, -1, 1, -1, 1,
.1, -1, 1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,
.1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1
		

Formula

Number triangle T(n,k)=sum{j=0..n, [j<=k]*[j<=n-k]*(-1)*(((-1)^(j+1)-0^(j+1))-((-1)^j-0^j))}.