A070259 Array f(m,n) read by antidiagonals: f(m,n) = minimal number of 0's in a 2m X 2n (0,1) matrix that contains no m X n submatrix of 1's (m >= 1, n >= 1).

4, 6, 6, 8, 7, 8, 10, 9, 9, 10, 12, 11, 10, 11, 12, 14, 13, 13, 13, 13, 14, 16, 15, 14, 13, 14, 15, 16, 18, 17, 16, 16, 16, 16, 17, 18, 20, 19, 18, 18, 16, 18, 18, 19, 20, 22, 21, 20, 19, 20, 20, 19, 20, 21, 22, 24, 23, 22, 21, 22, 19, 22, 21, 22, 23, 24, 26, 25, 24, 24, 24, 23

Offset

1,1

References

J. R. Griggs and C.-C. Ho, On the half-case of the Zarankiewicz problem, Discrete Math., 249 (2002), 95-104.

Links

Table of n, a(n) for n=1..72.

Example

Comment from Hermann Jamke: Array begins:
4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, ...
6, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, ...
8, 9, 10, 13, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, ...
10, 11, 13, 13, 16, 18, 19, 21, 24, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, ...
12, 13, 14, 16, 16, 20, 22, 24, 24, 26, 29, 32, 32, 34, 36, 39, 40, 42, 44, 46, ...
14, 15, 16, 18, 20, 19, 23, 25, 27, 29, 29, 31, 34, 37, 39, 39, 41, 43, 46, 49, ...
16, 17, 18, 19, 22, 23, 22, 26, 29, 31, 33, 34, 34, 36, 40, 42, 45, 47, 46, 48, ...
18, 19, 20, 21, 24, 25, 26, ...
20, 21, 22, 24, 24, 27, 29, ...
22, 23, 24, 25, 26, 29, 31, ...
24, 25, 26, 27, 29, 29, 33, ...
26, 27, 28, 29, 32, 31, 34, ...
28, 29, 30, 31, 32, 34, 34, ...
30, 31, 32, 33, 34, 37, 36, ...
32, 33, 34, 35, 36, 39, 40, ...
34, 35, 36, 37, 39, 39, 42, ...
36, 37, 38, 39, 40, 41, 45, ...
38, 39, 40, 41, 42, 43, 47, ...
40, 41, 42, 43, 44, 46, 46, ...
42, 43, 44, 45, 46, 49, 48, ...

Crossrefs

Cf. A070300.

Sequence in context: A200118 A254275 A074672 * A111653 A372786 A228363

Adjacent sequences: A070256 A070257 A070258 * A070260 A070261 A070262

Keyword

nonn,tabl

Author

N. J. A. Sloane, May 15 2002

Extensions

Reference gives first 7 rows of the array.

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008

Status

approved