A143255 Triangle read by rows, A128407 * A126988; 1<=k<=n.

1, -2, -1, -3, 0, -1, 0, 0, 0, 0, -5, 0, 0, 0, -1, 6, 3, 2, 0, 0, 1, -7, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 5, 0, 0, 2, 0, 0, 0, 0, 1, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 14, 7, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1

Offset

1,2

Comments

Left border = A055615: (1, -2, -3, 0, -5, 6, -7,...).

Right border = A008683, mu(n).

Row sums = A063441: (1, -3, -4, 0, -6, 12, 8,...).

Links

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

Formula

Triangle read by rows, A128407 * A126988; 1<=k<=n

t(n,m)=MoebiusMu[n]*A126988(n,m); t(n,m)=MoebiusMu[n]*If[m == 1, n, If[Mod[n, m] == 0, n/m, 0]]. - Roger L. Bagula, Sep 06 2008

Example

First few rows of the triangle =
1;
-2, -1;
-3, 0, -1;
0, 0, 0, 0;
-5, 0, 0, 0, -1;
6, 3, 2, 0, 0, 1;
-7, 0, 0, 0, 0, 0, -1;
0, 0, 0, 0, 0, 0, 0, 0;
0, 0, 0, 0, 0, 0, 0, 0, 0;
10, 5, 0, 0, 2, 0, 0, 0, 0, 1;
...

Mathematica

t[n_, m_] = MoebiusMu[n]*If[m == 1, n, If[Mod[n, m] == 0, n/m, 0]]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%] - Roger L. Bagula, Sep 06 2008

Crossrefs

Cf. A008683, A063441, A055615, A128407, A126988.

Cf. A128988.

Sequence in context: A202034 A323881 A062963 * A127139 A309103 A166139

Adjacent sequences: A143252 A143253 A143254 * A143256 A143257 A143258

Keyword

tabl,sign

Author

Gary W. Adamson, Aug 02 2008

Status

approved