A161364 Triangle read by rows, modified version of A161363; row sums = A000041.

1, 1, 0, 2, 0, 0, 2, 1, 0, 0, 4, 1, 0, 0, 0, 3, 2, 2, 0, 0, 0, 7, 2, 2, 0, 0, 0, 0, 7, 3, 2, 3, 0, 0, 0, 0, 12, 3, 4, 3, 0, 0, 0, 0, 0, 13, 5, 4, 3, 5, 0, 0, 0, 0, 0, 22, 6, 6, 3, 5, 0, 0, 0, 0, 0, 0, 2, 5, 7, 6, 6, 5, 7, 0, 0, 0, 0, 0, 0, 4, 9, 8, 6, 5, 7, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Gary W. Adamson, Jun 07 2009

Keywords

• nonn
• tabl

Comments

Row sums = A000041, the partition numbers.

Examples

			First few rows of the triangle =
1;
1, 0;
2, 0, 0;
2, 1, 0, 0;
4, 1, 0, 0, 0;
3, 2, 2, 0, 0, 0;
7, 2, 2, 0, 0, 0, 0;
7, 3, 2, 3, 0, 0, 0, 0;
12, 3, 4, 3, 0, 0, 0, 0, 0;
13, 5, 4, 3, 5, 0, 0, 0, 0, 0;
22, 6, 6, 3, 5, 0, 0, 0, 0, 0, 0;
25, 7, 6, 6, 5, 7, 0, 0, 0, 0, 0, 0;
42, 9, 8, 6, 5, 7, 0, 0, 0, 0, 0, 0, 0;
48, 13, 8, 9, 5, 7, 11, 0, 0, 0, 0, 0, 0, 0;
...
		

Crossrefs

A161363, A000041

Formula

Given triangle A161363, (the inverse of partition triangle A026794); multiply by (-1), delete right border of 1's, and shift down 1 row inserting a "1" at T(0,0); = triangle M. Let Q = an infinite lower triangular matrix with A000041 as the right border and the rest zeros. Triangle A161364 = M * Q.