A147768 Triangle read by rows: A000012^(-2) * A027293 as infinite lower triangular matrices.

1, -1, 1, 1, -1, 1, 0, 1, -1, 1, 1, 0, 1, -1, 1, 0, 1, 0, 1, -1, 1, 2, 0, 1, 0, 1, -1, 1, 0, 2, 0, 1, 0, 1, -1, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1, 4, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1, 2, 4, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1

Offset: 0

Author

Gary W. Adamson, Nov 11 2008

Keywords

• tabl
• sign

Comments

Row sums = A002865, (1, 0, 1, 1, 2, 2, 4, 4, 7, 8,...).

This triangle is the lower right half of a Toeplitz matrix. Each column of this triangle has the form [1, -1] U A053445. - Georg Fischer, Jul 28 2023

Examples

			First few rows of the triangle =
1;
-1, 1;
1, -1, 1;
0, 1, -1, 1;
1, 0, 1, -1, 1;
0, 1, 0, 1, -1, 1;
2, 0, 1, 0, 1, -1, 1;
0, 2, 0, 1, 0, 1, -1, 1;
3, 0, 2, 0, 1, 0, 1, -1, 1;
1, 3, 0, 2, 0, 1, 0, 1, -1, 1;
4, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1;
2, 4, 1, 3, 0, 2, 0, 1, 0, 1, -1, 1;
...
		

Crossrefs

Cf. A000012, A000041, A002865, A004736, A027293, A053445, A185018.

Formula

A000012^(-1) is the pairwise difference operator, and A027293 = a triangle with A000041 in every column.

Equals A185018 * A027293 since A000012^2 = A004736 and A004736^(-1) = A185018. - Georg Fischer, Jul 28 2023