A117355 Riordan array (1/(1-x^2),x(1-2x^2)/(1-x^2)).

1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, -1, 0, 1, 0, -1, 0, -2, 0, 1, 1, 0, -2, 0, -3, 0, 1, 0, -2, 0, -2, 0, -4, 0, 1, 1, 0, -2, 0, -1, 0, -5, 0, 1, 0, -3, 0, 0, 0, 1, 0, -6, 0, 1, 1, 0, -1, 0, 3, 0, 4, 0, -7, 0, 1, 0, -4, 0, 3, 0, 6, 0, 8, 0, -8, 0, 1, 1, 0, 1, 0, 6, 0, 8, 0, 13, 0, -9, 0, 1

Offset: 0

Author

Paul Barry, Mar 09 2006

Keywords

• easy
• sign
• tabl

Comments

Row sums are A077948.

Diagonal sums are the aerated version of A009545 with g.f. 1/(1-2x^2+2x^4).

Examples

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

Formula

Number triangle T(n,k)=sum{j=0..n-k, C(j-(n-k)/2-1,j)C(k,j)(1+(-1)^(n-k))/2}

T(n,k)=T(n-1,k-1)+T(n-2,k)-2*T(n-3,k-1), T(0,0)=T(1,1)=T(2,0)=T(2,2)=1, T(1,1)=T(2,1)=0, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Jan 16 2014