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%I #4 Feb 20 2016 09:14:51
%S 0,4,4,24,48,24,108,384,384,108,432,2736,5888,2736,432,1620,18336,
%T 80112,80112,18336,1620,5832,118032,1031344,2097552,1031344,118032,
%U 5832,20412,739008,12791896,52394312,52394312,12791896,739008,20412,69984,4533744
%N T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three exactly once.
%C Table starts
%C ......0.........4...........24.............108................432
%C ......4........48..........384............2736..............18336
%C .....24.......384.........5888...........80112............1031344
%C ....108......2736........80112.........2097552...........52394312
%C ....432.....18336......1031344........52394312.........2563440512
%C ...1620....118032.....12791896......1265974992.......121792778352
%C ...5832....739008....154606864.....29881402560......5665397992608
%C ..20412...4533744...1833130768....693021071760....259306140235672
%C ..69984..27384288..21416076480..15854541802056..11718368891185840
%C .236196.163381968.247279304248.358760880894864.524154208020159720
%H R. H. Hardin, <a href="/A269186/b269186.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -9*a(n-2)
%F k=2: a(n) = 10*a(n-1) -21*a(n-2) -20*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 8] for n>9
%F k=4: [order 16] for n>17
%F k=5: [order 40] for n>41
%e Some solutions for n=3 k=4
%e ..3..3..3..2. .2..3..1..3. .1..1..2..0. .2..2..2..3. .3..1..2..3
%e ..1..1..3..1. .2..3..3..2. .0..0..0..0. .0..0..2..0. .1..3..3..3
%e ..3..1..1..1. .3..3..2..2. .1..1..0..2. .2..2..0..0. .3..1..1..3
%Y Column 1 is A120908.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 20 2016
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