A145007 Eigentriangle of the partition numbers.

1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 2, 3, 0, -1, 0, 0, 3, 5, 0, -1, 0, 0, -1, 0, 0, 5, 7, 0, -1, 0, -2, 0, 0, 7, 11, 0, 0, -1, 0, -3, 0, 0, 11, 15, 0, 0, 0, -2, 0, -5, 0, 0, 15, 22, 0, 0, 0, 0, -3, 0, -7, 0, 0, 22, 30, 0, 0, 0, 0, 0, -5, 0, -11, 0, 0, 30, 42, 0, 1, 0, 0, 0, 0, -7, 0, -15, 0, 0, 42, 56

Offset: 0

Author

Gary W. Adamson, Sep 28 2008

Keywords

• eigen
• tabl
• sign

Comments

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

Row sums = the partition numbers, A000041, as well as the rightmost diagonal with no zeros.

Examples

			First few rows of the triangle =
1;
1, 0;
1, 1, 0;
0, 1, 2, 0;
0, 0, 2, 3, 0;
-1, 0, 0, 3, 5, 0;
0, -1, 0, 0, 5, 7, 0;
-1, 0, -2, 0, 0, 7, 11, 0,;
0, -1, 0, -3, 0, 0, 11, 15, 0;
0, 0, -2, 0, -5, 0, 0, 15, 22, 0;
0, 0, 0, -3, 0, -7, 0, 0, 22, 30, 0;
0, 0, 0, 0, -5, 0, -11, 0, 0, 30, 42, 0;
1, 0, 0, 0, 0, -7, 0, -15, 0, 0, 42, 56, 0;
0, 1, 0, 0, 0, 0, -11, 0, -22, 0, 0, 56, 77, 0;
0, 0, 2, 0, 0, 0, 0, -15, 0, -30, 0, 0, 77, 101, 0;
...
Example: row 4 = (0, 0, 2, 3) = termwise products of (0, 0, 1, 1) and (1, 1, 2, 3), where (0, 0, 1, 1) = row 4 of triangle A145006. The partition numbers = (1, 1, 2, 3, 5, 7, 11, 15,...).
		

Formula

Triangle read by rows, termwise products of A000041 (the partition numbers); and the partition number generator, A145006.