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%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
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