A183456 T(n,k) = Number of n X k binary arrays with every 1 having exactly three king-move neighbors equal to 1.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 6, 7, 7, 6, 1, 1, 9, 13, 10, 13, 9, 1, 1, 13, 23, 22, 22, 23, 13, 1, 1, 19, 37, 43, 60, 43, 37, 19, 1, 1, 28, 63, 73, 147, 147, 73, 63, 28, 1, 1, 41, 109, 139, 310, 439, 310, 139, 109, 41, 1, 1, 60, 183, 268, 723, 1077, 1077, 723, 268, 183

Offset

1,5

Comments

Nonzero solutions with other than 2X2 blocks of 1s first appear for k+n>=12 with both k>=5 and n>=5.

Table starts

.1..1...1...1....1.....1.....1......1.......1........1........1.........1

.1..2...3...4....6.....9....13.....19......28.......41.......60........88

.1..3...5...7...13....23....37.....63.....109......183......309.......527

.1..4...7..10...22....43....73....139.....268......487......904......1708

.1..6..13..22...60...147...310....723....1723.....3917.....8973.....20875

.1..9..23..43..147...439..1077...3005....8707....23625....64333....181321

.1.13..37..73..310..1077..2906...9511...32518....99333...312764...1046598

.1.19..63.139..723..3005..9511..36995..150145...547767..2049243...8099185

.1.28.109.268.1723..8707.32518.150145..739752..3285309.14656969..70963308

.1.41.183.487.3917.23625.99333.547767.3285309.16870217.90056146.543666294

Links

R. H. Hardin, Table of n, a(n) for n = 1..337

Example

Some solutions for 6X5
..0..0..0..0..0....0..0..0..0..0....0..0..1..1..0....0..0..0..0..0
..1..1..0..0..0....0..0..0..0..0....0..0..1..1..0....1..1..0..0..0
..1..1..0..0..0....1..1..0..0..0....0..0..0..0..0....1..1..0..0..0
..0..0..0..1..1....1..1..0..1..1....1..1..0..0..0....0..0..0..0..0
..1..1..0..1..1....0..0..0..1..1....1..1..0..1..1....1..1..0..1..1
..1..1..0..0..0....0..0..0..0..0....0..0..0..1..1....1..1..0..1..1

Crossrefs

Column 2 is A000930(n+1).

Column 3 is A003229.

Column 4 is A084386(n+1).

Column 5 is A183452.

Sequence in context: A329329 A306697 A297845 * A296313 A183342 A046688

Adjacent sequences: A183453 A183454 A183455 * A183457 A183458 A183459

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 05 2011

Status

approved