A152903 Convolution triangle: A152901 * (A152902 * 0^(n-k)).

1, -1, 3, -1, -3, 7, 0, -3, -7, 14, -1, 0, -7, -14, -1, 0, -7, -14, 1, -3, 0, -14, -27, 49, -1, 3, -7, 0, -27, -49, 88, 0, -3, 7, -14, 0, -49, -88, 155, 0, 0, -7, 14, -27, 0, -88, -155, 272, 1, 0, 0, -14, 27, -49, 0, -155, -272, 472

Offset: 1

Author

Gary W. Adamson, Dec 14 2008

Keywords

• tabl
• sign

Comments

Row sums = n, equivalent to the statement that A008683 convolved with A152902 = A000027, the natural numbers. Right border = A152902, left border = A008683.

Examples

			First few rows of the triangle =
1;
-1, 3;
-1, -3, 7;
0, -3, -7, 14;
-1, 0, -7, -14, 27;
1, -3, 0, -14, -27, 49;
-1, 3, -7, 0, -27, -49, 88;
0, -3, 7, -14, 0, -49, -88, 155;
0, 0, -7, 14, -27, 0, -88, -155, 272;
1, 0, 0, -14, 27, -49, 0, -155, -272, 472;
-1, 3, 0, 0, -27, 49, -88, 0, -272, -472, 819;
...
		

Crossrefs

Cf. A152901, A152902, A000027, A008683.

Formula

Triangle read by rows, A152901 * (A152902 * 0^(n-k); where triangle A152901 = a mu(n) "decrescendo" triangle with mu(n), A008683 in every column. (A152902 * 0^(n-k)) = a matrix with A152902 as the main diagonal and the rest zeros.