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%I #4 May 02 2018 08:06:02
%S 0,1,1,1,7,1,2,23,23,2,3,86,54,86,3,5,313,271,271,313,5,8,1145,842,
%T 1659,842,1145,8,13,4184,3420,7421,7421,3420,4184,13,21,15293,11916,
%U 39711,29479,39711,11916,15293,21,34,55895,45404,195279,200144,200144,195279
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3 or 4 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..0.....1......1.......2........3.........5..........8..........13...........21
%C ..1.....7.....23......86......313......1145.......4184.......15293........55895
%C ..1....23.....54.....271......842......3420......11916.......45404.......163979
%C ..2....86....271....1659.....7421.....39711.....195279.....1003855......5056641
%C ..3...313....842....7421....29479....200144.....992789.....5930552.....32529473
%C ..5..1145...3420...39711...200144...1541443....9758243....68015993....462257363
%C ..8..4184..11916..195279...992789...9758243...71307109...596704142...4824517709
%C .13.15293..45404.1003855..5930552..68015993..596704142..5846922441..56970820993
%C .21.55895.163979.5056641.32529473.462257363.4824517709.56970820993.668263785713
%H R. H. Hardin, <a href="/A303896/b303896.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2)
%F k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
%F k=3: [order 13] for n>14
%F k=4: [order 35] for n>40
%F k=5: [order 92] for n>98
%e Some solutions for n=5 k=4
%e ..0..0..0..1. .0..1..0..1. .0..0..1..1. .0..0..1..0. .0..1..1..0
%e ..0..1..1..1. .1..1..1..0. .1..0..0..0. .0..1..1..1. .0..1..1..1
%e ..1..1..1..1. .1..1..0..0. .0..1..0..0. .1..1..1..1. .1..0..1..1
%e ..1..0..0..0. .1..0..0..0. .1..1..1..1. .1..1..1..0. .0..0..0..1
%e ..0..0..0..1. .1..0..0..1. .0..1..0..0. .0..0..1..0. .1..0..1..0
%Y Column 1 is A000045(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, May 02 2018
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