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A297102 T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 4 king-move neighboring 1s. 8

%I

%S 2,4,4,8,16,8,16,58,58,16,32,216,351,216,32,64,808,2258,2258,808,64,

%T 128,3016,14566,26278,14566,3016,128,256,11264,93654,304059,304059,

%U 93654,11264,256,512,42080,602723,3498712,6316836,3498712,602723,42080,512

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

%C Table starts

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

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

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

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

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

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

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

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

%C .512.157192.24968616.5371615378.1145287856764.239124095978045.50370121334317960

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

%F Empirical for column k:

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

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

%F k=3: [order 20]

%F k=4: [order 47]

%e Some solutions for n=4 k=4

%e ..0..0..0..0. .0..1..0..1. .0..0..1..0. .0..1..1..1. .1..1..0..1

%e ..0..0..0..0. .0..0..0..1. .0..1..0..1. .1..0..0..0. .1..0..1..0

%e ..1..0..0..1. .1..0..1..0. .0..0..0..1. .1..1..0..0. .1..0..1..0

%e ..1..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..0..0. .1..1..0..1

%Y Column 1 is A000079.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 25 2017

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Last modified November 29 13:17 EST 2021. Contains 349416 sequences. (Running on oeis4.)