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%I #4 Jan 13 2018 11:25:34
%S 0,0,0,0,1,0,0,2,2,0,0,1,0,1,0,0,8,2,2,8,0,0,5,1,8,1,5,0,0,22,6,13,13,
%T 6,22,0,0,29,8,27,34,27,8,29,0,0,60,15,43,57,57,43,15,60,0,0,121,22,
%U 104,73,92,73,104,22,121,0,0,194,44,220,174,161,161,174,220,44,194,0,0,425,82
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .0..0..0...0...0...0....0....0....0.....0.....0.....0......0......0......0
%C .0..1..2...1...8...5...22...29...60...121...194...425....704...1421...2574
%C .0..2..0...2...1...6....8...15...22....44....82...152....267....486....898
%C .0..1..2...8..13..27...43..104..220...478...988..2085...4451...9505..20311
%C .0..8..1..13..34..57...73..174..350...800..1605..3376...7079..15234..32785
%C .0..5..6..27..57..92..161..369..918..2023..4177..9191..20759..46792.104465
%C .0.22..8..43..73.161..180..544.1076..2574..5208.11862..27724..63854.146389
%C .0.29.15.104.174.369..544.1404.2748..6157.13104.29303..63856.141487.313354
%C .0.60.22.220.350.918.1076.2748.4288.11715.22361.54254.112257.265785.593737
%H R. H. Hardin, <a href="/A298146/b298146.txt">Table of n, a(n) for n = 1..480</a>
%F Empirical for column k:
%F k=1: a(n) =
%F k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4)
%F k=3: a(n) = a(n-1) +2*a(n-2) +2*a(n-5) -4*a(n-6) -8*a(n-7) -a(n-8) +a(n-9)
%F k=4: [order 21] for n>27
%F k=5: [order 34] for n>40
%F k=6: [order 99] for n>106
%e Some solutions for n=7 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..0..0
%e ..0..1..1..0. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..1..0
%e ..1..0..1..0. .1..0..0..1. .0..1..1..0. .0..1..0..1. .1..0..0..1
%e ..1..0..1..0. .0..1..1..0. .1..0..0..0. .1..0..1..0. .0..1..1..0
%e ..1..0..1..0. .1..0..0..1. .0..1..1..1. .1..0..1..0. .0..0..1..0
%e ..1..0..0..1. .0..1..1..0. .1..0..0..1. .0..1..0..1. .1..0..1..0
%e ..1..1..1..1. .0..0..0..0. .1..1..0..0. .0..0..1..1. .1..1..0..0
%Y Column 2 is A297809.
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Jan 13 2018
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