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%I #4 May 27 2018 17:45:36
%S 1,2,2,4,8,4,8,21,21,8,16,49,24,49,16,32,120,54,54,120,32,64,293,108,
%T 116,108,293,64,128,719,236,253,253,236,719,128,256,1774,509,541,757,
%U 541,509,1774,256,512,4389,1091,1248,2050,2050,1248,1091,4389,512,1024,10893
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ...1....2....4....8....16.....32......64......128.......256........512
%C ...2....8...21...49...120....293.....719.....1774......4389......10893
%C ...4...21...24...54...108....236.....509.....1091......2363.......5109
%C ...8...49...54..116...253....541....1248.....2831......6471......14788
%C ..16..120..108..253...757...2050....5958....17002.....49275.....142734
%C ..32..293..236..541..2050...7062...26528....96528....359365....1331372
%C ..64..719..509.1248..5958..26528..135183...656194...3279365...16250652
%C .128.1774.1091.2831.17002..96528..656194..4217359..28101263..185066191
%C .256.4389.2363.6471.49275.359365.3279365.28101263.251711366.2221279211
%H R. H. Hardin, <a href="/A305230/b305230.txt">Table of n, a(n) for n = 1..511</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = 3*a(n-1) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
%F k=3: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -a(n-5) +2*a(n-6) for n>9
%F k=4: a(n) = a(n-1) +3*a(n-2) +a(n-3) -a(n-4) -3*a(n-5) -2*a(n-6) +2*a(n-7) for n>9
%F k=5: [order 12] for n>16
%F k=6: [order 17] for n>22
%F k=7: [order 28] for n>35
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0. .0..1..1..1
%e ..0..0..1..0. .0..1..0..0. .0..0..0..0. .0..1..0..0. .1..1..1..1
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
%e ..0..0..0..0. .0..0..1..0. .0..1..0..0. .1..0..0..0. .0..0..0..0
%e ..0..0..0..1. .0..0..0..0. .0..0..0..0. .1..1..0..0. .0..0..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A303721.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, May 27 2018
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