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

Author

Gary W. Adamson, Aug 02 2008

Keywords

• tabl
• sign

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,...).

Examples

			Triangle begins:
  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;
  ...
		

Crossrefs

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

Cf. A128988.

Programs

Mathematica

t[n_, m_] = MoebiusMu[n]*If[m == 1, n, If[Mod[n, m] == 0, n/m, 0]]; Table[t[n, m], {n, 1, 14}, {m, 1, n}] // Flatten (* Roger L. Bagula, Sep 06 2008 *)

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(n mod m == 0, n/m, 0)). - Roger L. Bagula, Sep 06 2008