%I #4 Jan 24 2018 10:29:13
%S 1,1,1,1,1,1,1,0,0,1,1,1,3,1,1,1,2,1,1,2,1,1,1,5,2,5,1,1,1,8,8,2,2,8,
%T 8,1,1,5,7,9,20,9,7,5,1,1,22,25,13,38,38,13,25,22,1,1,29,25,26,84,169,
%U 84,26,25,29,1,1,60,58,74,319,238,238,319,74,58,60,1,1,121,95,134,770,1019,978
%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1..1..1..1...1....1.....1.....1......1.......1.......1........1.........1
%C .1..1..0..1...2....1.....8.....5.....22......29......60......121.......194
%C .1..0..3..1...5....8.....7....25.....25......58......95......155.......299
%C .1..1..1..2...2....9....13....26.....74.....134.....325......731......1568
%C .1..2..5..2..20...38....84...319....770....2106....6301....17282.....47774
%C .1..1..8..9..38..169...238..1019...3112....7518...25887....74736....218787
%C .1..8..7.13..84..238...978..3895..11843...49752..184380...640323...2550161
%C .1..5.25.26.319.1019..3895.22938..81474..386923.1791871..7595552..35648606
%C .1.22.25.74.770.3112.11843.81474.329249.1693779.9364144.43238329.235861179
%H R. H. Hardin, <a href="/A298667/b298667.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>5
%F k=3: [order 12]
%F k=4: [order 35]
%e Some solutions for n=8 k=4
%e ..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
%e ..1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e ..0..1..1..1. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..1
%e ..1..1..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..0..1
%e ..1..1..1..1. .1..1..1..1. .1..0..1..1. .1..1..0..1. .1..1..1..1
%e ..0..1..1..0. .0..1..1..0. .1..1..1..0. .0..1..1..1. .0..1..1..0
%e ..1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..1
%e ..0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0. .0..1..1..0
%Y Column 2 is A297809(n-2).
%K nonn,tabl
%O 1,13
%A _R. H. Hardin_, Jan 24 2018
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