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%I #4 Mar 17 2017 12:01:13
%S 2,4,4,8,16,8,16,61,64,16,32,233,409,256,32,64,896,2776,2837,1024,64,
%T 128,3444,19220,35373,19776,4096,128,256,13225,131617,456316,448490,
%U 137459,16384,256,512,50789,901397,5742620,10741381,5676420,955680,65536,512
%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.
%C Table starts
%C ...2.....4.......8........16...........32.............64..............128
%C ...4....16......61.......233..........896...........3444............13225
%C ...8....64.....409......2776........19220.........131617...........901397
%C ..16...256....2837.....35373.......456316........5742620.........72394838
%C ..32..1024...19776....448490.....10741381......247708452.......5724272337
%C ..64..4096..137459...5676420....252014450....10634931992.....449942735521
%C .128.16384..955680..71903903...5921518755...457711375590...35481195059121
%C .256.65536.6645662.910712188.139111379622.19691576356912.2796411775700471
%H R. H. Hardin, <a href="/A283857/b283857.txt">Table of n, a(n) for n = 1..221</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 4*a(n-1)
%F k=3: [order 8]
%F k=4: [order 17]
%F k=5: [order 45]
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1)
%F n=2: a(n) = 3*a(n-1) +a(n-2) +7*a(n-3) +6*a(n-4)
%F n=3: [order 14]
%F n=4: [order 28]
%F n=5: [order 74]
%e Some solutions for n=4 k=4
%e ..1..0..0..1. .0..0..1..0. .1..1..1..1. .0..0..0..0. .1..0..1..1
%e ..0..1..1..0. .1..0..0..0. .0..1..0..0. .0..0..0..1. .1..0..1..1
%e ..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..1
%e ..1..1..0..0. .1..0..0..0. .1..0..0..1. .1..1..0..1. .1..1..0..1
%Y Column 1 is A000079.
%Y Column 2 is A000302.
%Y Row 1 is A000079.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 17 2017
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