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%I #4 Jul 14 2016 09:53:53
%S 1,1,2,2,6,3,4,16,18,6,8,48,46,54,12,16,144,137,146,162,24,32,432,401,
%T 570,450,486,48,64,1296,1152,2185,2334,1428,1458,96,128,3888,3336,
%U 8273,11624,9774,4463,4374,192,256,11664,9720,31495,57984,64045,40572,14086
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (0,-1) (-1,-2) or (-2,0) and new values introduced in order 0..2.
%C Table starts
%C ...1.....1......2.......4........8.........16..........32...........64
%C ...2.....6.....16......48......144........432........1296.........3888
%C ...3....18.....46.....137......401.......1152........3336.........9720
%C ...6....54....146.....570.....2185.......8273.......31495.......120845
%C ..12...162....450....2334....11624......57984......290927......1465435
%C ..24...486...1428....9774....64045.....421793.....2788663.....18527905
%C ..48..1458...4463...40572...351197....3056856....26631796....233894638
%C ..96..4374..14086..169348..1931619...22207559...255796423...2976710318
%C .192.13122..44195..704704.10581148..160767947..2451632155..37779884891
%C .384.39366.139130.2937764.58059378.1166126087.23548292980.480461388679
%H R. H. Hardin, <a href="/A275037/b275037.txt">Table of n, a(n) for n = 1..338</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) for n>3
%F k=2: a(n) = 3*a(n-1) for n>2
%F k=3: [order 16] for n>17
%F k=4: [order 35] for n>37
%F k=5: [order 70] for n>74
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) for n>2
%F n=2: a(n) = 3*a(n-1) for n>3
%F n=3: [order 9] for n>10
%F n=4: [order 17] for n>19
%F n=5: [order 28] for n>32
%F n=6: [order 67] for n>72
%e Some solutions for n=4 k=4
%e ..0..1..2..1. .0..1..2..1. .0..1..0..1. .0..1..0..2. .0..1..0..2
%e ..1..0..1..2. .2..0..1..0. .2..0..2..0. .0..1..2..0. .0..2..1..0
%e ..1..2..0..2. .1..0..1..2. .2..0..1..2. .1..2..1..0. .1..0..2..0
%e ..0..1..2..0. .1..2..0..1. .1..2..1..2. .1..2..0..1. .2..0..2..1
%Y Column 1 is A003945(n-2).
%Y Column 2 is A008776(n-1).
%Y Row 1 is A000079(n-2).
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_, Jul 14 2016
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