A077052 Right Moebius transformation matrix, M, by antidiagonals.

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

Offset: 1

Author

Clark Kimberling, Oct 22 2002

Keywords

• sign
• tabl

Comments

If S=(s(1),s(2),...) is a sequence written as a row vector, then S*M is the Moebius transform of S; i.e. its n-th term is Sum{mu(k)*s(k): k|n}. M is the transpose of the left Moebius transformation matrix, A077050.

Examples

			Northwest corner:
1 -1 -1 0 -1 1
0 1 0 -1 0 -1
0 0 1 0 0 -1
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
		

Crossrefs

Cf. A077049, A077050, A077051.

Formula

M=T^(-1), where T is the right summatory matrix, A077051.