A071676 Array read by antidiagonals of signed variant of trinomial coefficients with T(n,k)=T(n-1,k)+T(n-1,k-1)-T(n-1,k-2) starting with T(0,0)=1.

1, 0, 1, 0, 1, 1, 0, -1, 2, 1, 0, 0, -1, 3, 1, 0, 0, -2, 0, 4, 1, 0, 0, 1, -5, 2, 5, 1, 0, 0, 0, 0, -8, 5, 6, 1, 0, 0, 0, 3, -5, -10, 9, 7, 1, 0, 0, 0, -1, 8, -15, -10, 14, 8, 1, 0, 0, 0, 0, 2, 11, -30, -7, 20, 9, 1, 0, 0, 0, 0, -4, 15, 6, -49, 0, 27, 10, 1, 0, 0, 0, 0, 1, -10, 41, -14, -70, 12, 35, 11, 1, 0, 0, 0, 0, 0, -5, -6, 77, -56, -90, 30, 44

Offset: 0

Author

Henry Bottomley, May 30 2002

Keywords

• sign
• tabl

Comments

Each column is eventually positive, i.e. for each k there is a number j(k) such that T(n,k) is positive for all n>=j(k). Despite this, each row sum is 1.

Examples

			Rows start:
1, 0,  0,  0,  0, ...;
1, 1, -1,  0,  0, 0, ...;
1, 2, -1, -2,  1, 0,  0, ...;
1, 3,  0, -5,  0, 3, -1,  0, ...;
1, 4,  2, -8, -5, 8,  2, -4, 1, ...;
etc...
		

Crossrefs

Cf. A071675.