0,3

The matrix generated by this matrix has row sums F(n+1).

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

Matrix begins

0, 1,

2, -1, 1,

3, 0, -1, 1,

4, 0, 0, -1, 1,

5, 0, 0, 0, -1, 1,

6, 0, 0, 0, 0, -1, 1,

7, 0, 0, 0, 0, 0, -1, 1,

8, 0, 0, 0, 0, 0, 0, -1, 1,

9, 0, 0, 0, 0, 0, 0, 0, -1, 1

The row augmented triangular matrix

1,

0, 1,

2, -1, 1,

3, 0, -1, 1,

4, 0, 0, -1, 1,

5, 0, 0, 0, -1, 1,

6, 0, 0, 0, 0, -1, 1,

7, 0, 0, 0, 0, 0, -1, 1,

8, 0, 0, 0, 0, 0, 0, -1, 1,

9, 0, 0, 0, 0, 0, 0, 0, -1, 1

has row sums 0^n+n. Its inverse has row sums (n+1)(2-n)/2 or A080956. This is the matrix

1,

0, 1,

-2, 1, 1,

-5, 1, 1, 1,

-9, 1, 1, 1, 1,

-14, 1, 1, 1, 1, 1,

-20, 1, 1, 1, 1, 1, 1,

-27, 1, 1, 1, 1, 1, 1, 1,

-35, 1, 1, 1, 1, 1, 1, 1, 1

with first column (n+2)(1-n)/2.

Cf. A155727.

Sequence in context: A028306 A111259 A138948 this_sequence A105400 A033774 A033804

Adjacent sequences: A155723 A155724 A155725 this_sequence A155727 A155728 A155729

sign,tabf

Paul Barry (pbarry(AT)wit.ie), Jan 25 2009