editing

approved

R. H. Hardin, <a href="/A297102/b297102.txt">Table of n, a(n) for n = 1..180</a>

allocated for R. H. Hardin

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

1,1

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

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]

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

Column 1 is A000079.

allocated

nonn,tabl

R. H. Hardin, Dec 25 2017

approved

editing

allocated for R. H. Hardin

allocated

approved