A144257 Weight array of A086270.

1, 2, 0, 3, 1, 0, 4, 2, 1, 0, 5, 3, 2, 1, 0, 6, 4, 3, 2, 1, 0, 7, 5, 4, 3, 2, 1, 0, 8, 6, 5, 4, 3, 2, 1, 0, 9, 7, 6, 5, 4, 3, 2, 1, 0, 10, 8, 7, 6, 5, 4, 3, 2, 1, 0, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 12, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 12, 11, 10, 9, 8, 7, 6, 5

Offset: 1

Author

Clark Kimberling, Sep 16 2008

Keywords

• nonn
• tabl

Comments

For the definition of weight array, see A144112.

From Gary W. Adamson, Feb 18 2010: (Start)

Identical to an infinite lower triangular matrix with (1,2,3,...) in every column but the leftmost column shifted one row upwards, giving:

1;

2, 0;

3, 1, 0;

4, 2, 1, 0;

5, 3, 2, 1, 0;

...

Let the triangle = M. Row sums = A000124; M * [1,2,3,...] = A050407 starting with offset 3: (1, 2, 5, 11, 21, 36, ...); and lim_{n->inf} M^n = the odd-indexed Fibonacci numbers, A001519: (1, 2, 5, 13, ...). (End)

Examples

			Northwest corner:
  1 2 3 4 5 6 7 8 9
  0 1 2 3 4 5 6 7 8
  0 1 2 3 4 5 6 7 8
  0 1 2 3 4 5 6 7 8
  0 1 2 3 4 5 6 7 8
		

Crossrefs

Cf. A086270.

Cf. A000124, A050407, A001519. - Gary W. Adamson, Feb 18 2010

Formula

Row 1 = A000027. All subsequent rows are 0 followed by A000027.