A152904 Triangle read by rows: T(n,k) = A008683(n-k+1); 1<=k<=n; mu(n) "decrescendo".

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

Offset: 1

Author

Gary W. Adamson, Dec 14 2008

Keywords

• tabl
• sign

Examples

			Triangle begins
   1;
  -1, 1;
  -1, -1, 1;
   0, -1, -1, 1;
  -1, 0, -1, -1, 1;
   1, -1, 0, -1, -1, 1;
  -1, 1, -1, 0, -1, -1, 1;
   0, -1, 1, -1, 0, -1, -1, 1;
   0, 0, -1, 1, -1, 0, -1, -1, 1;
   ...
Production matrix begins
  -1, 1,
  -2, 0, 1,
  -3, 0, 0, 1,
  -6, 0, 0, 0, 1,
  -9, 0, 0, 0, 0, 1,
  -17, 0, 0, 0, 0, 0, 1,
  -28, 0, 0, 0, 0, 0, 0, 1,
  -50, 0, 0, 0, 0, 0, 0, 0, 1,
  -83, 0, 0, 0, 0, 0, 0, 0, 0, 1,
  -147, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ...
  where first column is -A073776(n+1). - _Paul Barry_, Feb 10 2011
		

Links

• E. Deutsch, L. Ferrari and S. Rinaldi, Production Matrices, Advances in Applied Mathematics, 34 (2005) pp. 101-122.

Crossrefs

Cf. A008683, A002321, A073776, A152901, A152902.

Row sums = A002321, the Mertens function. A185694 is an eigensequence.

Formula

Triangle read by rows, T(n,k) = A008683(n-k+1) = A008683 in every column = A008683 "decrescendo"d by rows.