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%I #4 Jul 10 2018 15:06:32
%S 1,2,2,4,4,4,8,3,3,8,16,5,8,5,16,32,8,9,9,8,32,64,13,21,23,21,13,64,
%T 128,21,42,44,44,42,21,128,256,34,81,125,88,125,81,34,256,512,55,165,
%U 313,359,359,313,165,55,512,1024,89,330,773,1125,2081,1125,773,330,89,1024,2048
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 6, 7 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........1024
%C ...2..4...3....5.....8.....13......21.......34........55.........89.........144
%C ...4..3...8....9....21.....42......81......165.......330........657........1317
%C ...8..5...9...23....44....125.....313......773......1964.......4948.......12456
%C ..16..8..21...44....88....359....1125.....3117.....10022......31545.......95424
%C ..32.13..42..125...359...2081....9442....38020....174483.....785604.....3427907
%C ..64.21..81..313..1125...9442...61454...342508...2212378...14109348....86477928
%C .128.34.165..773..3117..38020..342508..2431114..21261766..184273462..1497908640
%C .256.55.330.1964.10022.174483.2212378.21261766.257262996.3099570150.34685951835
%H R. H. Hardin, <a href="/A316693/b316693.txt">Table of n, a(n) for n = 1..420</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1)
%F k=2: a(n) = a(n-1) +a(n-2) for n>4
%F k=3: a(n) = a(n-1) +a(n-2) +2*a(n-3) for n>6
%F k=4: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) +a(n-4) -2*a(n-5) -6*a(n-6) -4*a(n-7) for n>11
%F k=5: [order 7] for n>11
%F k=6: [order 16] for n>21
%F k=7: [order 46] for n>52
%e Some solutions for n=5 k=4
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
%e ..0..1..1..0. .0..1..1..0. .0..0..0..0. .0..0..1..0. .0..0..0..0
%e ..1..0..0..1. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..1..0
%e ..1..1..1..1. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0
%e ..1..1..1..1. .0..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..0
%Y Column 1 is A000079(n-1).
%Y Column 2 is A000045(n+1).
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jul 10 2018
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