

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.


2



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
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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



