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%I #4 Aug 13 2018 14:34:08
%S 1,1,1,1,2,1,1,2,2,1,1,3,8,3,1,1,6,21,21,6,1,1,17,86,140,86,17,1,1,46,
%T 377,905,905,377,46,1,1,124,1648,6179,10563,6179,1648,124,1,1,341,
%U 7261,42793,116212,116212,42793,7261,341,1,1,947,31969,297043,1304057,2098813
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C .1...1.....1.......1.........1...........1............1..............1
%C .1...2.....2.......3.........6..........17...........46............124
%C .1...2.....8......21........86.........377.........1648...........7261
%C .1...3....21.....140.......905........6179........42793.........297043
%C .1...6....86.....905.....10563......116212......1304057.......14683085
%C .1..17...377....6179....116212.....2098813.....37826270......685931021
%C .1..46..1648...42793...1304057....37826270...1097286743....32035215365
%C .1.124..7261..297043..14683085...685931021..32035215365..1507709268026
%C .1.341.31969.2056698.165135266.12431437346.933917327711.70833352314014
%H R. H. Hardin, <a href="/A318045/b318045.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 3*a(n-1) -a(n-2) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6) for n>7
%F k=3: [order 21] for n>23
%F k=4: [order 72] for n>74
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..1..0..1. .0..0..1..0. .0..0..1..1. .0..1..0..1
%e ..1..0..1..0. .1..1..1..0. .0..1..0..1. .0..1..0..0. .1..1..0..0
%e ..0..1..1..0. .0..1..0..1. .1..0..1..0. .1..0..0..1. .0..0..1..1
%e ..0..1..0..1. .1..0..0..1. .0..1..1..0. .1..1..0..0. .1..1..0..0
%e ..1..0..1..0. .1..0..1..0. .1..0..0..1. .0..1..0..1. .0..1..0..1
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Aug 13 2018
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