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A282528 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its king-move neighbors. 8

%I

%S 2,4,4,8,15,8,16,43,43,16,32,144,206,144,32,64,473,1097,1097,473,64,

%T 128,1529,5675,10041,5675,1529,128,256,5004,29433,86258,86258,29433,

%U 5004,256,512,16335,153037,747184,1207312,747184,153037,16335,512,1024,53283

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

%C Table starts

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

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

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

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

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

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

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

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

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

%C .1024.173960.21444844.4264923086.699393940820.119296756793024.20559180796734866

%H R. H. Hardin, <a href="/A282528/b282528.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

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

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

%F 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)

%F k=4: [order 14]

%F k=5: [order 31]

%F k=6: [order 68]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 17 2017

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Last modified August 3 15:54 EDT 2021. Contains 346439 sequences. (Running on oeis4.)