A178408 Triangle T(n,k) read by rows. Each column is the Mobius function "recurrence" with the previous column as input.

1, 0, -1, 0, -1, 0, 0, -1, 1, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 4, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0

Offset: 1

Author

Mats Granvik, May 27 2010

Keywords

• sign
• tabl

Comments

The title says "recurrence" in quotes because the Mobius function does not have a regular recurrence. Row sums are A008683. Number of nonzero elements in the rows are A086436 which is essentially the same as A001222. Each row is a row in a Pascal like triangle.

Examples

			Table begins:
1,
0,-1,
0,-1,0,
0,-1,1,0,
0,-1,0,0,0,
0,-1,2,0,0,0,
0,-1,0,0,0,0,0,
0,-1,2,-1,0,0,0,0,
0,-1,1,0,0,0,0,0,0,
0,-1,2,0,0,0,0,0,0,0,
		

Crossrefs

Cf. A008683, A086436, A001222.