A155726 Production matrix for Fibonacci numbers, read by row.

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

Offset: 0

Author

Paul Barry, Jan 25 2009

Keywords

• sign
• tabf

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A080956, A155727.