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
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.
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