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%I
%S 1,2,2,4,6,4,8,14,14,8,16,35,45,35,16,32,95,133,133,95,32,64,257,419,
%T 569,419,257,64,128,700,1382,2227,2227,1382,700,128,256,1907,4495,
%U 9063,12039,9063,4495,1907,256,512,5202,14754,37030,60157,60157,37030,14754,5202
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2.....4......8......16........32.........64.........128..........256
%C ...2....6....14.....35......95.......257........700........1907.........5202
%C ...4...14....45....133.....419......1382.......4495.......14754........48525
%C ...8...35...133....569....2227......9063......37030......153117.......634563
%C ..16...95...419...2227...12039.....60157.....304184.....1569163......8067785
%C ..32..257..1382...9063...60157....400016....2495323....16110625....103827789
%C ..64..700..4495..37030..304184...2495323...20241433...163342483...1322465254
%C .128.1907.14754.153117.1569163..16110625..163342483..1699138124..17279766046
%C .256.5202.48525.634563.8067785.103827789.1322465254.17279766046.223853493247
%H R. H. Hardin, <a href="/A318024/b318024.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -2*a(n-4) -a(n-6) +a(n-7)
%F k=3: [order 18] for n>23
%F k=4: [order 70] for n>74
%e Some solutions for n=5 k=4
%e ..0..1..1..1. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..1..1
%e ..1..1..1..0. .1..0..0..1. .1..1..0..0. .0..0..0..0. .0..1..1..1
%e ..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..1..1..1. .1..1..1..0
%e ..1..1..1..1. .1..0..0..0. .0..1..0..0. .0..1..1..1. .1..1..0..0
%e ..1..1..1..1. .0..1..0..0. .1..1..0..0. .0..1..1..1. .1..0..0..0
%Y Column 1 is A000079(n-1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Aug 12 2018
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