A084934 Rectangular array T(m,n) (m>=1, n>=1) read by antidiagonals: row m consists of the numbers ( i + mj : i >= 0, j >= 0 ), sorted in increasing order, with repetitions allowed.

0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 2, 2, 2, 1, 0, 2, 3, 3, 2, 1, 0, 3, 3, 3, 3, 2, 1, 0, 3, 4, 4, 4, 3, 2, 1, 0, 3, 4, 4, 4, 4, 3, 2, 1, 0, 3, 4, 5, 5, 5, 4, 3, 2, 1, 0, 4, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, 4, 5, 6, 6, 6, 6, 5, 4, 3, 2, 1, 0, 4, 5, 6, 6, 6, 6, 6, 5, 4, 3, 2, 1, 0, 4, 6, 6, 7, 7, 7, 7, 6, 5, 4, 3, 2, 1, 0

Offset: 1

Author

Clark Kimberling, Jun 12 2003

Keywords

• nonn
• tabl

Comments

The combinatorial limit of the rows is the sequence of nonnegative integers.

Examples

			The northwest corner includes
m\n 1 2 3 4 5 6 7 8 9 10 ...
----------------------------
1 | 0 1 1 2 2 2 3 3 3 3 ...
2 | 0 1 2 2 3 3 4 4 4 5 ...
3 | 0 1 2 3 3 4 4 5 5 6 ...
4 | 0 1 2 3 4 4 5 5 6 6 ...
5 | 0 1 2 3 4 5 5 6 6 7 ...
Row m=0, for example, consists of the numbers i+j (i>=0, j>=0), sorted.
		

Crossrefs

Cf. A010766, A084934.

Formula

For k>=0, the number of k's in row m is [(k+1)/m].

Extensions

Edited by N. J. A. Sloane, May 19 2007