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%I #4 Jul 20 2018 13:33:39
%S 1,1,1,1,4,1,1,8,8,1,1,24,25,24,1,1,82,139,139,82,1,1,272,818,1595,
%T 818,272,1,1,908,4869,17947,17947,4869,908,1,1,3076,29339,207116,
%U 384535,207116,29339,3076,1,1,10444,177688,2403703,8450612,8450612,2403703
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1.......1.........1...........1..............1................1
%C .1.....4.......8........24..........82............272..............908
%C .1.....8......25.......139.........818...........4869............29339
%C .1....24.....139......1595.......17947.........207116..........2403703
%C .1....82.....818.....17947......384535........8450612........186574154
%C .1...272....4869....207116.....8450612......354399907......14920072888
%C .1...908...29339...2403703...186574154....14920072888....1197129513001
%C .1..3076..177688..27979008..4130997988...629855730272...96317261216226
%C .1.10444.1078090.325990496.91552460948.26612973830635.7756014658872472
%H R. H. Hardin, <a href="/A317065/b317065.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 14] for n>16
%F k=4: [order 38] for n>40
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..0..1. .0..1..1..0. .0..0..1..1. .0..1..1..1
%e ..1..1..0..1. .1..0..0..0. .0..1..1..0. .1..1..0..0. .1..1..0..0
%e ..1..0..0..1. .0..0..0..1. .1..1..0..1. .0..0..1..0. .1..0..0..1
%e ..1..0..0..1. .1..1..1..0. .0..0..0..0. .1..1..1..1. .0..1..1..0
%e ..0..1..0..1. .0..1..0..1. .1..0..1..1. .0..0..1..0. .0..1..0..1
%Y Column 2 is A303882.
%Y Column 3 is A305680.
%Y Column 4 is A305681.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 20 2018
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