A282528 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its king-move neighbors.

2, 4, 4, 8, 15, 8, 16, 43, 43, 16, 32, 144, 206, 144, 32, 64, 473, 1097, 1097, 473, 64, 128, 1529, 5675, 10041, 5675, 1529, 128, 256, 5004, 29433, 86258, 86258, 29433, 5004, 256, 512, 16335, 153037, 747184, 1207312, 747184, 153037, 16335, 512, 1024, 53283

Offset

1,1

Comments

Table starts

....2......4........8.........16...........32..............64...............128

....4.....15.......43........144..........473............1529..............5004

....8.....43......206.......1097.........5675...........29433............153037

...16....144.....1097......10041........86258..........747184...........6509805

...32....473.....5675......86258......1207312........17100576.........243903065

...64...1529....29433.....747184.....17100576.......398640091........9355397095

..128...5004...153037....6509805....243903065......9355397095......361721564040

..256..16335...794716...56491269...3461268322....218250094269....13881707109180

..512..53283..4128244..490864610..49204976763...5103468618577...534350790960907

.1024.173960.21444844.4264923086.699393940820.119296756793024.20559180796734866

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -8*a(n-4)

k=3: a(n) = 5*a(n-1) +2*a(n-2) -a(n-3) -24*a(n-4) +13*a(n-5) -2*a(n-7) +6*a(n-8)

k=4: [order 14]

k=5: [order 31]

k=6: [order 68]

Example

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

Crossrefs

Column 1 is A000079.

Sequence in context: A216950 A240364 A225982 * A297094 A283282 A181253

Adjacent sequences: A282525 A282526 A282527 * A282529 A282530 A282531

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 17 2017

Status

approved