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%I #4 Jan 23 2017 12:55:03
%S 0,0,0,0,0,0,1,4,4,1,2,104,290,104,2,9,612,2919,2919,612,9,34,3056,
%T 14561,15624,14561,3056,34,124,16368,63840,52529,52529,63840,16368,
%U 124,432,82656,245037,146956,130646,146956,245037,82656,432,1464,397040,871492
%N T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its king-move neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
%C Table starts
%C ....0.......0.......0.......1.......2.......9.......34......124......432
%C ....0.......0.......4.....104.....612....3056....16368....82656...397040
%C ....0.......4.....290....2919...14561...63840...245037...871492..2953605
%C ....1.....104....2919...15624...52529..146956...385284...979866..2440042
%C ....2.....612...14561...52529..130646..290073...610493..1274531..2667156
%C ....9....3056...63840..146956..290073..560972..1066920..2001002..3797780
%C ...34...16368..245037..385284..610493.1066920..1935368..3474958..6171868
%C ..124...82656..871492..979866.1274531.2001002..3474958..6195904.10767665
%C ..432..397040.2953605.2440042.2667156.3797780..6171868.10767665.18777294
%C .1464.1873344.9666482.5946178.5549073.7294930.11158871.18503172.31737730
%H R. H. Hardin, <a href="/A281540/b281540.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -6*a(n-2) -16*a(n-3) +12*a(n-4) +24*a(n-5) +8*a(n-6) for n>10
%F k=2: [order 12]
%F k=3: [order 22] for n>30
%F k=4: [order 36] for n>50
%e Some solutions for n=4 k=4
%e ..0..1..0..1. .0..1..0..2. .0..1..0..1. .0..1..0..1. .0..0..1..0
%e ..2..2..0..2. .2..2..1..2. .2..1..0..2. .2..1..2..2. .1..2..1..0
%e ..1..1..1..1. .0..1..0..1. .0..0..2..1. .2..0..0..1. .0..0..2..0
%e ..2..0..2..0. .0..2..2..2. .1..1..0..1. .1..2..2..1. .1..2..1..1
%Y Column 1 is A280309.
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Jan 23 2017
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