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A275037 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.

%I A275037 #4 Jul 14 2016 09:53:53
%S A275037 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 A275037 570,450,486,48,64,1296,1152,2185,2334,1428,1458,96,128,3888,3336,
%U A275037 8273,11624,9774,4463,4374,192,256,11664,9720,31495,57984,64045,40572,14086
%N A275037 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 A275037 Table starts
%C A275037 ...1.....1......2.......4........8.........16..........32...........64
%C A275037 ...2.....6.....16......48......144........432........1296.........3888
%C A275037 ...3....18.....46.....137......401.......1152........3336.........9720
%C A275037 ...6....54....146.....570.....2185.......8273.......31495.......120845
%C A275037 ..12...162....450....2334....11624......57984......290927......1465435
%C A275037 ..24...486...1428....9774....64045.....421793.....2788663.....18527905
%C A275037 ..48..1458...4463...40572...351197....3056856....26631796....233894638
%C A275037 ..96..4374..14086..169348..1931619...22207559...255796423...2976710318
%C A275037 .192.13122..44195..704704.10581148..160767947..2451632155..37779884891
%C A275037 .384.39366.139130.2937764.58059378.1166126087.23548292980.480461388679
%H A275037 R. H. Hardin, <a href="/A275037/b275037.txt">Table of n, a(n) for n = 1..338</a>
%F A275037 Empirical for column k:
%F A275037 k=1: a(n) = 2*a(n-1) for n>3
%F A275037 k=2: a(n) = 3*a(n-1) for n>2
%F A275037 k=3: [order 16] for n>17
%F A275037 k=4: [order 35] for n>37
%F A275037 k=5: [order 70] for n>74
%F A275037 Empirical for row n:
%F A275037 n=1: a(n) = 2*a(n-1) for n>2
%F A275037 n=2: a(n) = 3*a(n-1) for n>3
%F A275037 n=3: [order 9] for n>10
%F A275037 n=4: [order 17] for n>19
%F A275037 n=5: [order 28] for n>32
%F A275037 n=6: [order 67] for n>72
%e A275037 Some solutions for n=4 k=4
%e A275037 ..0..1..2..1. .0..1..2..1. .0..1..0..1. .0..1..0..2. .0..1..0..2
%e A275037 ..1..0..1..2. .2..0..1..0. .2..0..2..0. .0..1..2..0. .0..2..1..0
%e A275037 ..1..2..0..2. .1..0..1..2. .2..0..1..2. .1..2..1..0. .1..0..2..0
%e A275037 ..0..1..2..0. .1..2..0..1. .1..2..1..2. .1..2..0..1. .2..0..2..1
%Y A275037 Column 1 is A003945(n-2).
%Y A275037 Column 2 is A008776(n-1).
%Y A275037 Row 1 is A000079(n-2).
%K A275037 nonn,tabl
%O A275037 1,3
%A A275037 _R. H. Hardin_, Jul 14 2016