A160756 Triangle read by rows, infinite lower triangular Toeplitz matrix with A078008 in every column convolved with A001333.

1, 0, 1, 2, 0, 1, 2, 2, 0, 3, 6, 2, 2, 0, 7, 10, 6, 2, 6, 0, 17, 22, 10, 6, 6, 14, 0, 41, 42, 22, 10, 18, 14, 34, 0, 99, 86, 42, 22, 30, 42, 34, 82, 0, 239, 170, 86, 42, 66, 70, 102, 82, 198, 0, 577

Offset: 0

Author

Gary W. Adamson, May 25 2009

Keywords

• nonn
• tabl

Comments

Row sums = A001333: (1, 1, 3, 7, 17, 41,...). Sum of n-th row terms = rightmost term of next row.

Examples

			First few rows of the triangle =
1;
0, 1;
2, 0, 1;
2, 2, 0, 3;
6, 2, 2, 0, 7;
10, 6, 2, 6, 0, 17;
22, 10, 6, 6, 14, 0, 41;
42, 22, 10, 18, 14, 34, 0, 99;
86, 42, 22, 30, 42, 34, 82, 0, 239;
170, 86, 42, 66, 70, 102, 82, 198, 0, 577;
...
Example: row 4 = (6, 2, 2, 0, 7) = (6, 2, 2, 0, 1) * (1, 1, 1, 3, 7).
		

Crossrefs

Cf. A078008, A001333

Formula

Let M = an infinite lower triangular Toeplitz matrix with A078008 (1, 0, 2, 2, 6, 10, 22, 42, 86, 170,...). Let Q = the eigensequence of that triangle prefaced with a 1: (1, 1, 1, 3, 7, 17,...) where A001333 = (1, 1, 3, 7, 17,...). The triangle = M * Q.