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T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal and vertical neighbors.
7

%I #4 Mar 01 2017 09:53:24

%S 2,4,4,8,16,8,16,57,57,16,32,209,378,209,32,64,768,2521,2521,768,64,

%T 128,2816,16818,30824,16818,2816,128,256,10329,112276,376359,376359,

%U 112276,10329,256,512,37889,749447,4598361,8402216,4598361,749447,37889,512

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

%C Table starts

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

%C ....4.....16........57..........209............768..............2816

%C ....8.....57.......378.........2521..........16818............112276

%C ...16....209......2521........30824.........376359...........4598361

%C ...32....768.....16818.......376359........8402216.........187671790

%C ...64...2816....112276......4598361......187671790........7664347268

%C ..128..10329....749447.....56176300.....4191671248......312996735204

%C ..256..37889...5002276....686250407....93617080958....12781345612180

%C ..512.138980..33388996...8383419717..2090880805128...521941108563948

%C .1024.509792.222863968.102414019954.46698565884588.21314084605931116

%H R. H. Hardin, <a href="/A283130/b283130.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5)

%F k=3: [order 9]

%F k=4: [order 17]

%F k=5: [order 48]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Diagonal is A068471.

%Y Column 1 is A000079.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 01 2017