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

1,7

Comments

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

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

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.

Sequence in context: A143667 A299485 A246785 * A125927 A285864 A092869

Adjacent sequences: A084931 A084932 A084933 * A084935 A084936 A084937

Keyword

nonn,tabl

Author

Clark Kimberling, Jun 12 2003

Extensions

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

Status

approved