A115292 Correlation triangle for (1+x)^3/(1-x).

1, 4, 4, 7, 17, 7, 8, 32, 32, 8, 8, 39, 66, 39, 8, 8, 40, 88, 88, 40, 8, 8, 40, 95, 130, 95, 40, 8, 8, 40, 96, 152, 152, 96, 40, 8, 8, 40, 96, 159, 194, 159, 96, 40, 8, 8, 40, 96, 160, 216, 216, 160, 96, 40, 8, 8, 40, 96, 160, 223, 258, 223, 160, 96, 40, 8

Offset: 0

Author

Paul Barry, Jan 19 2006

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A115293. Diagonal sums are A115294. T(2n,n) is A115295. T(2n,n)-T(2n,n+1) is 1,10,27,35,35,35,... The transform of (-1)^n by this matrix is 1,0,-3,0,4,0,-4,0,4,...

Examples

			Triangle begins
1;
4, 4;
7, 17, 7;
8, 32, 32, 8;
8, 39, 66, 39, 8;
8, 40, 88, 88, 40, 8;
8, 40, 95, 130, 95, 40, 8;
8, 40, 96, 152, 152, 96, 40, 8;
		

Formula

G.f.: (1+x)^3*(1+xy)^3/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*A115291(k-j)*[j<=n-k]*A115291(n-k-j)}.