A222456 T(n,k) = Number of n X k 0..1 arrays with exactly floor(n X k/2) elements unequal to at least one horizontal, vertical or antidiagonal neighbor, with new values introduced in row major 0..1 order.

1, 0, 0, 0, 0, 0, 3, 2, 2, 3, 4, 7, 2, 7, 4, 4, 10, 17, 17, 10, 4, 5, 23, 27, 101, 27, 23, 5, 20, 64, 194, 426, 426, 194, 64, 20, 27, 175, 467, 1722, 1847, 1722, 467, 175, 27, 48, 400, 2375, 8483, 16440, 16440, 8483, 2375, 400, 48, 63, 983, 6320, 46788, 84558, 161779, 84558

Offset

1,7

Comments

Table starts

...1....0......0........3..........4............4..............5

...0....0......2........7.........10...........23.............64

...0....2......2.......17.........27..........194............467

...3....7.....17......101........426.........1722...........8483

...4...10.....27......426.......1847........16440..........84558

...4...23....194.....1722......16440.......161779........1752892

...5...64....467.....8483......84558......1752892.......17977932

..20..175...2375....46788.....910358.....18608623......398308251

..27..400...6320...246899....4757427....201223272.....4297235804

..48..983..31706..1263032...51324484...2201719251....98149697258

..63.2498..84949..6568737..271866564..24272631638..1083889273467

.175.6409.426134.34802586.2984245628.268705232398.25078137790680

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Example

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

Crossrefs

Column 1 is A222283.

Sequence in context: A029246 A316995 A338241 * A222673 A222666 A335401

Adjacent sequences: A222453 A222454 A222455 * A222457 A222458 A222459

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 20 2013

Status

approved