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%I #4 Feb 21 2016 08:57:46
%S 0,4,0,24,108,0,108,1368,1620,0,432,13896,46872,20412,0,1620,127512,
%T 1104264,1365336,236196,0,5832,1104264,23549400,74853576,36673560,
%U 2598156,0,20412,9211608,474819408,3719884392,4684312584,938176344
%N T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
%C Table starts
%C .0........4..........24............108...............432................1620
%C .0......108........1368..........13896............127512.............1104264
%C .0.....1620.......46872........1104264..........23549400...........474819408
%C .0....20412.....1365336.......74853576........3719884392........174924572760
%C .0...236196....36673560.....4684312584......542973139128......59587625651904
%C .0..2598156...938176344...279339197256....75556007986536...19356924219624936
%C .0.27634932.23230366488.16128206816904.10181956012212600.6090616046325570480
%H R. H. Hardin, <a href="/A269276/b269276.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 18*a(n-1) -81*a(n-2)
%F k=3: a(n) = 42*a(n-1) -441*a(n-2)
%F k=4: a(n) = 98*a(n-1) -2401*a(n-2) for n>3
%F k=5: a(n) = 234*a(n-1) -14277*a(n-2) +68796*a(n-3) -86436*a(n-4)
%F k=6: [order 6] for n>7
%F k=7: [order 10] for n>11
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -9*a(n-2)
%F n=2: a(n) = 14*a(n-1) -49*a(n-2) for n>4
%F n=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>7
%F n=4: [order 8] for n>12
%F n=5: [order 18] for n>23
%F n=6: [order 40] for n>46
%e Some solutions for n=3 k=4
%e ..0..2..0..1. .0..0..0..0. .0..2..0..0. .0..0..0..0. .0..0..2..0
%e ..0..2..3..1. .2..2..0..0. .2..2..3..1. .2..0..2..1. .0..2..2..3
%e ..2..1..0..2. .3..2..1..1. .0..1..0..2. .0..0..1..3. .3..1..1..0
%Y Row 1 is A120908.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Feb 21 2016
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