A183397 T(n,k)=Half the number of nXk binary arrays with no element equal to a strict majority of its knight-move neighbors

1, 2, 2, 4, 8, 4, 8, 8, 8, 8, 16, 8, 46, 8, 16, 32, 8, 69, 69, 8, 32, 64, 8, 227, 156, 227, 8, 64, 128, 32, 794, 451, 451, 794, 32, 128, 256, 128, 2701, 2595, 2145, 2595, 2701, 128, 256, 512, 288, 9816, 12150, 17689, 17689, 12150, 9816, 288, 512, 1024, 648, 34649, 58407

Offset

1,2

Comments

Same solutions for no element unequal to a strict majority of its neighbors, via xor with a 0101... checkerboard pattern

Table starts

...1...2......4.......8......16.......32.......64......128.......256......512

...2...8......8.......8.......8........8.......32......128.......288......648

...4...8.....46......69.....227......794.....2701.....9816.....34649...120536

...8...8.....69.....156.....451.....2595....12150....58407....280852..1405171

..16...8....227.....451....2145....17689...115241...776298...5449079.38642644

..32...8....794....2595...17689...233505..2051732.19639561.204306894

..64..32...2701...12150..115241..2051732.25401329

.128.128...9816...58407..776298.19639561

.256.288..34649..280852.5449079

.512.648.120536.1405171

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Example

Some solutions with a(1,1)=0 for 6X5
..0..1..1..0..0....0..0..0..1..0....0..0..0..0..0....0..1..1..1..0
..0..1..1..0..0....1..0..1..1..0....0..1..0..0..0....0..0..1..1..1
..0..1..1..0..1....0..0..1..1..0....1..1..1..1..1....0..0..0..0..1
..0..1..0..0..0....1..0..1..1..0....0..1..0..1..1....1..1..0..0..1
..1..1..1..0..1....0..0..1..1..0....0..0..0..0..0....1..1..0..0..1
..0..1..0..1..1....1..0..1..1..0....1..1..1..1..0....1..1..0..0..1

Crossrefs

Sequence in context: A368515 A366714 A359488 * A339490 A281469 A302623

Adjacent sequences: A183394 A183395 A183396 * A183398 A183399 A183400

Keyword

nonn,tabl

Author

R. H. Hardin Jan 04 2011

Status

approved