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%I #4 Jun 30 2018 19:10:23
%S 1,1,1,1,4,1,1,8,8,1,1,24,13,24,1,1,82,60,60,82,1,1,272,217,418,217,
%T 272,1,1,908,749,2186,2186,749,908,1,1,3076,2822,12281,16817,12281,
%U 2822,3076,1,1,10444,10516,72713,128585,128585,72713,10516,10444,1,1,35480,38934
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1.....1.......1........1..........1...........1.............1
%C .1.....4.....8......24.......82........272.........908..........3076
%C .1.....8....13......60......217........749........2822.........10516
%C .1....24....60.....418.....2186......12281.......72713........423041
%C .1....82...217....2186....16817.....128585.....1076888.......8858964
%C .1...272...749...12281...128585....1396959....16730969.....194865364
%C .1...908..2822...72713..1076888...16730969...294007902....4935143895
%C .1..3076.10516..423041..8858964..194865364..4935143895..118878261056
%C .1.10444.38934.2465234.72193958.2259023326.82582592407.2848273549547
%H R. H. Hardin, <a href="/A316376/b316376.txt">Table of n, a(n) for n = 1..180</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 20] for n>21
%F k=4: [order 70] for n>72
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..0..1. .0..0..1..1. .0..1..1..1. .0..1..0..0
%e ..0..1..1..0. .1..1..1..0. .1..1..0..0. .0..1..0..0. .0..1..1..1
%e ..1..1..1..0. .1..0..1..0. .1..1..1..1. .0..1..1..0. .1..1..0..1
%e ..0..1..1..0. .1..0..0..0. .0..0..1..1. .0..1..1..0. .1..0..0..1
%e ..1..0..1..0. .0..1..0..1. .1..1..0..0. .1..0..0..1. .1..0..0..1
%Y Column 2 is A303882.
%Y Column 3 is A304546.
%Y Column 4 is A304547.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jun 30 2018
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