A176202 Convolution triangle, row sums = A000041. M = A000041 in each column with two interleaved zeros; Q = A000726 diagonalized with the rest zeros. A176202 = M*Q.

1, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 1, 0, 0, 4, 0, 0, 2, 0, 0, 5, 2, 0, 0, 2, 0, 0, 7, 0, 2, 0, 0, 4, 0, 0, 9, 0, 0, 4, 0, 0, 5, 0, 0, 13, 3, 0, 0, 4, 0, 0, 7, 0, 0, 16, 0, 3, 0, 0, 8, 0, 0, 9, 0, 0, 22, 0, 0, 6, 0, 0, 10, 0, 0, 13, 0, 0, 27

Offset: 0

Author

Gary W. Adamson, Apr 11 2010

Keywords

• nonn
• tabl

Comments

Row sums = A000041

Examples

			First few rows of the triangle =
1;
0, 1;
0, 0, 2;
1, 0, 0, 2;
0, 1, 0, 0, 4;
0, 0, 2, 0, 0, 5;
2, 0, 0, 2, 0, 0, 7;
0, 2, 0, 0, 4, 0, 0, 9;
0, 0, 4, 0, 0, 5, 0, 0, 13;
3, 0, 0, 4, 0, 0, 7, 0, 0, 16;
0, 3, 0, 0, 8, 0, 0, 9, 0, 0, 22;
0, 0, 6, 0, 0, 10, 0, 0, 13, 0, 0, 27;
5, 0, 0, 6, 0, 0, 14, 0, 0, 16, 0, 0, 36;
0, 5, 0, 0, 12, 0, 0, 18, 0, 0, 22, 0, 0, 44;
0, 0, 10, 0, 0, 15, 0, 0, 26, 0, 0, 27, 0, 0, 57;
7, 0, 0, 10, 0, 0, 21, 0, 0, 32, 0, 0, 36, 0, 0, 70;
0, 7, 0, 0, 20, 0, 0, 27, 0, 0, 44, 0, 0, 44, 0, 0, 89;
0, 0, 14, 0, 0, 25, 0, 0, 39, 0, 0, 54, 0, 0, 57, 0, 0, 108;
11, 0, 0, 14, 0, 0, 35, 0, 0, 48, 0, 0, 72, 0, 0, 70, 0, 0, 135;
...
		

Crossrefs

Cf. A000041, A000726, A113685, A174714

Formula

Let M = an infinite lower triangular matrix with A000041 interleaved with two

zeros in each column. Q = A000726 diagonalized, with the rest zeros. A176202

= M*Q