A174888 Triangle read by rows. Row sums = Mobius function A008683, row counts of nonzero elements = A074206.

1, 0, -1, 0, -1, 0, 1, -1, 0, 0, 0, -1, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 1, 0, 0

Offset: 1

Author

Mats Granvik, Apr 01 2010

Keywords

• sign
• tabl

Comments

This table cannot be completed as a triangle beyond row 95 because the ordered factorization value for 96 is 112, which is greater than the row length 96. Values in the first column are either zero or one, and are chosen so that the number of nonzero elements in each row equals A074206 while rows sums equals A008683. The row indices for nonzero elements in the 1st column are A174891.

Examples

			Table begins:
n\k|....1....2....3....4....5....6....7....8....9...10
---|--------------------------------------------------
1..|....1
2..|....0...-1
3..|....0...-1....0
4..|....1...-1....0....0
5..|....0...-1....0....0....0
6..|....1...-1....1....0....0....0
7..|....0...-1....0....0....0....0....0
8..|....1...-1....1...-1....0....0....0....0
9..|....1...-1....0....0....0....0....0....0....0
10.|....1...-1....1....0....0....0....0....0....0....0
Notice that the 30th row begins with a zero:
0,-1,1,-1,1,-1,1,-1,1,-1,1,-1,1,-1
		

Crossrefs

Cf. A008683, A074206, A174889, A174891, A174892.

Formula

First column = A174889.

Beginning from the second column: a(n)=if k<=A074206 then ((-1)^(k+1)) else 0.