A204851 Triangle by rows relating to A005773.

1, 1, 1, 2, 2, 1, 5, 5, 2, 1, 13, 13, 6, 2, 1, 35, 35, 16, 7, 2, 1, 96, 96, 45, 19, 8, 2, 1, 267, 267, 126, 56, 22, 9, 2, 1, 750, 750, 357, 160, 68, 25, 10, 2, 1, 2123, 2123, 1016, 463, 198, 81, 28, 11, 2, 1, 6046, 6046, 2907, 1337, 586, 240, 95, 31, 12, 2, 1

Offset: 0

Author

Gary W. Adamson, Jan 19 2012

Keywords

• nonn
• tabl

Comments

Left border = A005773. Row sums = A005773 with offset 1

Examples

			First few rows of the triangle =
1;
1, 1;
2, 2, 1;
5, 5, 2, 1;
13, 13, 6, 2, 1;
35, 35, 16, 7, 2, 1;
96, 96, 45, 19, 8, 2, 1;
267, 267, 126, 56, 22, 9, 2, 1;
750, 750, 357, 160, 68, 25, 10, 2, 1;
2123, 2123, 1016, 463, 198, 81, 28, 11, 2, 1;
6046, 6046, 2907, 1337, 586, 240, 95, 31, 12, 2, 1;
...
Row 3 = (5, 5, 2, 1) since the top row of M^3 = [5, 5, 2, 1, 0, 0, 0,...]
		

Crossrefs

Cf. A005773

Formula

n-th row of the triangle is the top row of M^n, deleting the zeros; where M = the infinite square production matrix:

1, 1, 0, 0, 0, 0, 0,...

1, 1, 1, 0, 0, 0, 0,...

1, 1, 0, 1, 0, 0, 0,...

1, 1, 1, 0, 1, 0, 0,...

1, 1, 1, 1, 0, 1, 0,...

1, 1, 1, 1, 1, 0, 1,...

1, 1, 1, 1, 1, 1, 0,...

...