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

1,4

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

Links

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

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

Example

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

Crossrefs

Column 1 is A006367(n-1).

Sequence in context: A330590 A055097 A258751 * A279902 A331004 A278540

Adjacent sequences: A280230 A280231 A280232 * A280234 A280235 A280236

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 29 2016

Status

approved