A145580 Eigentriangle, row sums = A000930.

1, 1, 1, 0, 1, 2, -1, 0, 2, 3, 0, -1, 0, 3, 4, 1, 0, -2, 0, 4, 6, 0, 1, 0, -3, 0, 6, 9, -1, 0, 2, 0, -4, 0, 9, 13, 0, -1, 0, 3, 0, -6, 0, 13, 19, 1, 0, -2, 0, 4, 0, -9, 0, 19, 28

Offset: 1

Author

Gary W. Adamson, Oct 13 2008

Keywords

• tabl
• sign

Comments

Row sums = A000930 starting with offset 1: (1, 1, 2, 3, 4, 6, 9, 13, 19,...).

Sum of n-th row terms = rightmost term of next row.

Examples

			First few rows of the triangle =
1;
1, 1;
0, 1, 2;
-1, 0, 2, 3;
0, -1, 0, 3, 4;
1, 0, -2, 0, 4, 6;
0, 1, 0, -3, 0, 6, 9;
-1, 0, 2, 0, -4, 0, 9, 13;
0, -1, 0, 3, 0, -6, 0, 13, 19;
1, 0, -2, 0, 4, 0, -9, 0, 19, 28;
...
Row 6 = (1, 0, -2, 0, 4, 6) = termwise products of (1, 0, -1, 0, 1, 1) and (1, 1, 2, 3, 4, 6).
		

Crossrefs

A000930

Formula

Let M = an infinite lower triangular matrix with (1, 1, 0, -1, 0, 1, 0, -1, 0, 1,...) in every column; and X = an infinite lower triangular matrix with A000930 as the main diagonal (offset 1): (1, 1, 2, 3, 4, 6, 9, 13, 19,...) and the rest zeros. Triangle A145580 = M * X.