A213418 T(n,k) = Half the number of n X k binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 253, 128, 16, 32, 512, 1970, 1970, 512, 32, 64, 2048, 15109, 28952, 15109, 2048, 64, 128, 8192, 114302, 407498, 407498, 114302, 8192, 128, 256, 32768, 854473, 5524088, 10142461, 5524088, 854473, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

...1......2.........4............8............16.............32.............64

...2......8........32..........128...........512...........2048...........8192

...4.....32.......253.........1970.........15109.........114302.........854473

...8....128......1970........28952........407498........5524088.......72544970

..16....512.....15109.......407498......10142461......235950302.....5190742489

..32...2048....114302......5524088.....235950302.....9107867048...323797652462

..64...8192....854473.....72544970....5190742489...323797652462.18095156337973

.128..32768...6323090....927723512..109049720858.10764286026008

.256.131072..46390429..11603925098.2205335209381

.512.524288.337896422.142479782648

Links

R. H. Hardin, Table of n, a(n) for n = 1..96

R. P. Anstee, Properties of (0,1)-matrices with no triangles, J. Combin. Theory Ser. A 29 (1980), no. 2, 186--198.

H. J. Ryser, Combinatorial configurations, SIAM J. Appl. Math. 17 1969 593--602.

Example

Some solutions for n=4 k=4
..0..1..1..0....1..0..1..1....0..1..0..0....1..0..1..0....1..0..0..0
..1..1..0..0....1..0..1..0....1..0..1..1....0..0..0..1....0..1..1..0
..0..1..0..0....1..1..0..0....1..0..0..1....1..0..1..0....1..0..1..1
..0..1..1..0....0..1..0..0....1..0..1..1....1..0..1..1....1..1..1..1

Crossrefs

Sequence in context: A300208 A303421 A301407 * A317517 A300182 A317532

Adjacent sequences: A213415 A213416 A213417 * A213419 A213420 A213421

Keyword

nonn,tabl

Author

R. H. Hardin and N. J. A. Sloane, Jun 10 2012

Status

approved