A283130 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal and vertical neighbors.

2, 4, 4, 8, 16, 8, 16, 57, 57, 16, 32, 209, 378, 209, 32, 64, 768, 2521, 2521, 768, 64, 128, 2816, 16818, 30824, 16818, 2816, 128, 256, 10329, 112276, 376359, 376359, 112276, 10329, 256, 512, 37889, 749447, 4598361, 8402216, 4598361, 749447, 37889, 512

Offset

1,1

Comments

Table starts

....2......4.........8...........16.............32................64

....4.....16........57..........209............768..............2816

....8.....57.......378.........2521..........16818............112276

...16....209......2521........30824.........376359...........4598361

...32....768.....16818.......376359........8402216.........187671790

...64...2816....112276......4598361......187671790........7664347268

..128..10329....749447.....56176300.....4191671248......312996735204

..256..37889...5002276....686250407....93617080958....12781345612180

..512.138980..33388996...8383419717..2090880805128...521941108563948

.1024.509792.222863968.102414019954.46698565884588.21314084605931116

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

k=3: [order 9]

k=4: [order 17]

k=5: [order 48]

Example

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

Crossrefs

Diagonal is A068471.

Column 1 is A000079.

Sequence in context: A262338 A368043 A283691 * A295716 A282399 A297374

Adjacent sequences: A283127 A283128 A283129 * A283131 A283132 A283133

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 01 2017

Status

approved