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

0,1

Comments

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

Links

Table of n, a(n) for n=0..86.

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))}.

Example

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

Crossrefs

Sequence in context: A246016 A306638 A076479 * A209661 A033999 A000012

Adjacent sequences: A155037 A155038 A155039 * A155041 A155042 A155043

Keyword

easy,sign,tabl

Author

Paul Barry, Jan 19 2009

Status

approved