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%I #6 Jun 21 2022 23:47:22
%S 1,2,2,4,8,4,8,32,32,8,16,128,232,128,16,32,512,1708,1708,512,32,64,
%T 2048,12576,23672,12576,2048,64,128,8192,92616,327848,327848,92616,
%U 8192,128,256,32768,682084,4543028,8525992,4543028,682084,32768,256,512,131072
%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1......2........4...........8............16...............32
%C ...2......8.......32.........128...........512.............2048
%C ...4.....32......232........1708.........12576............92616
%C ...8....128.....1708.......23672........327848..........4543028
%C ..16....512....12576......327848.......8525992........221935656
%C ..32...2048....92616.....4543028.....221935656......10857946336
%C ..64...8192...682084....62956480....5777358820.....531234388944
%C .128..32768..5023328...872451104..150397035552...25991845818768
%C .256.131072.36995208.12090455460.3915165237488.1271713349901092
%H R. H. Hardin, <a href="/A301443/b301443.txt">Table of n, a(n) for n = 1..286</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: a(n) = 8*a(n-1) -4*a(n-2) -5*a(n-3);
%F k=4: [order 11];
%F k=5: [order 31];
%F k=6: [order 97] for n>98.
%e Some solutions for n=5, k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
%e ..0..0..1..0. .0..1..1..1. .0..1..0..1. .0..1..0..1. .0..0..1..0
%e ..1..0..1..0. .0..0..1..1. .0..1..1..1. .1..1..0..1. .1..1..1..0
%e ..1..0..1..0. .1..0..0..0. .1..0..0..1. .0..1..0..1. .1..0..0..0
%e ..1..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A004171(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 21 2018
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