A110314 Inverse of number triangle related to Fibonacci numbers.

1, -1, 1, -2, -2, 1, 0, -6, -3, 1, 0, 0, -12, -4, 1, 0, 0, 0, -20, -5, 1, 0, 0, 0, 0, -30, -6, 1, 0, 0, 0, 0, 0, -42, -7, 1, 0, 0, 0, 0, 0, 0, -56, -8, 1, 0, 0, 0, 0, 0, 0, 0, -72, -9, 1, 0, 0, 0, 0, 0, 0, 0, 0, -90, -10, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -110, -11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -132, -12, 1

Offset: 0

Author

Paul Barry, Jul 19 2005

Keywords

• easy
• sign
• tabl

Comments

Row sums are 1-n^2 with g.f. (1-3x)/(1-x)^3. Diagonal sums are A110315. Inverse of A039948.

Examples

			Rows begin
1;
-1,1;
-2,-2,1;
0,-6,-3,1;
0,0,-12,-4,1;
0,0,0,-20,-5,1;
0,0,0,0,-30,-6,1;
		

Formula

T(n, k)=if(n=k, 1, if(n-k=1, -binomial(n, 1), if(n-k=2, -2*binomial(n, 2), 0)))