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T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,4,0,2,1 for x=0,1,2,3,4

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`%I #5 Mar 31 2012 12:36:26
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`%S 1,1,1,2,7,2,3,10,10,3,5,23,27,23,5,8,57,76,76,57,8,13,122,248,391,
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`%T 248,122,13,21,275,735,1895,1895,735,275,21,34,623,2178,8118,15289,
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`%U 8118,2178,623,34,55,1394,6622,37661,97292,97292,37661,6622,1394,55,89,3133,20006
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`%N T(n,k)=Number of nXk 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,4,0,2,1 for x=0,1,2,3,4
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`%C Every 0 is next to 0 3's, every 1 is next to 1 4's, every 2 is next to 2 0's, every 3 is next to 3 2's, every 4 is next to 4 1's
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`%C Table starts
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`%C ..1....1.....2.......3.........5...........8...........13.............21
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`%C ..1....7....10......23........57.........122..........275............623
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`%C ..2...10....27......76.......248.........735.........2178...........6622
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`%C ..3...23....76.....391......1895........8118........37661.........172339
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`%C ..5...57...248....1895.....15289.......97292.......689313........4940279
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`%C ..8..122...735....8118.....97292......965315.....10183698......109227468
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`%C .13..275..2178...37661....689313....10183698....163282859.....2644969245
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`%C .21..623..6622..172339...4940279...109227468...2644969245....65251102177
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`%C .34.1394.20006..791490..34729760..1156876986..42258577643..1581794578196
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`%C .55.3133.60256.3631677.244473481.12249728518.676570815905.38383334376131
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`%H R. H. Hardin, <a href="/A196653/b196653.txt">Table of n, a(n) for n = 1..219</a>
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`%e Some solutions for n=6 k=4
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`%e ..0..2..0..0....0..0..0..0....2..0..0..0....2..0..2..0....2..0..0..2
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`%e ..0..2..2..2....0..0..2..2....0..1..2..0....0..0..2..2....0..0..0..0
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`%e ..0..0..0..0....0..0..1..0....1..4..1..2....0..0..0..0....0..0..2..2
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`%e ..0..1..0..0....0..1..4..1....0..1..0..0....2..0..0..0....0..2..2..0
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`%e ..1..4..1..0....0..0..1..0....0..2..2..2....2..0..2..2....2..2..0..0
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`%e ..0..1..0..0....0..0..0..2....2..0..0..0....0..0..2..0....0..0..0..2
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`%Y Column 1 is A000045
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`%Y Column 2 is A196316
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`%K nonn,tabl
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`%O 1,4
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`%A _R. H. Hardin_ Oct 04 2011
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