A143153 Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.

1, -1, 2, -1, 0, 3, 0, -2, 0, 2, -1, 0, 0, 0, 5, 1, -2, -3, 0, 0, 2, -1, 0, 0, 0, 0, 0, 7, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0, 0, 0, 3, 1, -2, 0, 0, -5, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1, -2, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 2

Offset

1,3

Comments

Right border = A020639, Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11,...).

Left border = mu(n), A008683: (1, -1, -1, 0, -1, 1, -1,...).

Row sums = a signed version of A097945: (1, -1, -2, 0, -4, 2, -6,...) such that parity = (+) iff mu(n) = +.

Links

Table of n, a(n) for n=1..105.

Formula

Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n; where A020639 = Lpf(n): (1, 2, 3, 2, 5, 2, 7, 2, 3, 2,...) and A054525 = the Mobius transform.

Example

First few rows of the triangle =
1;
-1, 2;
-1, 0, 3;
0, -2, 0, 2;
-1, 0, 0, 0, 5;
1, -2, -3, 0, 0, 2;
-1, 0, 0, 0, 0, 0, 7;
0, 0, 0, -2, 0, 0, 0, 2;
0, 0, -3, 0, 0, 0, 0, 0, 3;
1, -2, 0, 0, -5, 0, 0, 0, 0, 2;
-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11;
0, 2, 0, -2, 0, -2, 0, 0, 0, 0, 0, 2;
...

Crossrefs

Cf. A008683, A097945, A020639, A054525.

Sequence in context: A050464 A014405 A368464 * A127448 A128179 A356749

Adjacent sequences: A143150 A143151 A143152 * A143154 A143155 A143156

Keyword

tabl,sign

Author

Gary W. Adamson & Mats Granvik, Jul 27 2008

Status

approved