A280233 T(n,k)=Number of nXk 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 4, 2, 2, 6, 6, 2, 5, 8, 9, 8, 5, 8, 14, 16, 16, 14, 8, 15, 24, 29, 48, 29, 24, 15, 26, 42, 52, 116, 116, 52, 42, 26, 46, 72, 95, 288, 355, 288, 95, 72, 46, 80, 124, 168, 678, 1102, 1102, 678, 168, 124, 80, 139, 212, 298, 1600, 3376, 4260, 3376, 1600, 298, 212

Offset: 1

Author

R. H. Hardin, Dec 29 2016

Keywords

• nonn
• tabl

Comments

Table starts

..0...0...2....2.....5......8......15.......26........46.........80.........139

..0...4...6....8....14.....24......42.......72.......124........212.........362

..2...6...9...16....29.....52......95......168.......298........522.........911

..2...8..16...48...116....288.....678.....1600......3766.......8704.......20040

..5..14..29..116...355...1102....3376.....9860.....29091......84644......244759

..8..24..52..288..1102...4260...16282....59648....220330.....806580.....2928596

.15..42..95..678..3376..16282...80825...377706...1780344....8321484....38431266

.26..72.168.1600..9860..59648..377706..2212304..13139746...77599244...451789710

.46.124.298.3766.29091.220330.1780344.13139746..98743448..738470180..5428286449

.80.212.522.8704.84644.806580.8321484.77599244.738470180.7008698040.65195901946

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A006367(n-1).

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>5

k=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>7

k=3: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) for n>7

k=4: [order 16] for n>19

k=5: [order 22] for n>25