A297102 T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 4 king-move neighboring 1s.

2, 4, 4, 8, 16, 8, 16, 58, 58, 16, 32, 216, 351, 216, 32, 64, 808, 2258, 2258, 808, 64, 128, 3016, 14566, 26278, 14566, 3016, 128, 256, 11264, 93654, 304059, 304059, 93654, 11264, 256, 512, 42080, 602723, 3498712, 6316836, 3498712, 602723, 42080, 512

Offset

1,1

Comments

Table starts

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

...4.....16.......58........216...........808............3016.............11264

...8.....58......351.......2258.........14566...........93654............602723

..16....216.....2258......26278........304059.........3498712..........40369420

..32....808....14566.....304059.......6316836.......129966319........2685011300

..64...3016....93654....3498712.....129966319......4769336288......175908737504

.128..11264...602723...40369420....2685011300....175908737504....11598374165583

.256..42080..3879430..465695460...55461279894...6486806363511...764506387012021

.512.157192.24968616.5371615378.1145287856764.239124095978045.50370121334317960

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 20]

k=4: [order 47]

Example

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

Crossrefs

Column 1 is A000079.

Sequence in context: A295716 A282399 A297374 * A283415 A283857 A227442

Adjacent sequences: A297099 A297100 A297101 * A297103 A297104 A297105

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 25 2017

Status

approved