%I #4 Jul 26 2016 14:54:00

%S 1,2,2,5,9,3,14,54,16,6,41,324,84,31,12,122,1944,444,178,63,24,365,

%T 11664,2344,1011,394,129,48,1094,69984,12376,5758,2404,1017,260,96,

%U 3281,419904,65344,32771,14884,8122,2645,534,192,9842,2519424,345008,186538,91849

%N T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,1) and new values introduced in order 0..2.

%C Table starts

%C ...1....2.....5......14.......41.......122.........365.........1094

%C ...2....9....54.....324.....1944.....11664.......69984.......419904

%C ...3...16....84.....444.....2344.....12376.......65344.......345008

%C ...6...31...178....1011.....5758.....32771......186538......1061795

%C ..12...63...394....2404....14884.....91849......566331......3495079

%C ..24..129..1017....8122....65045....518049.....4142271.....33102260

%C ..48..260..2645...27373...283169...2940064....30551417....317215507

%C ..96..534..6980...94065..1266905..17159883...232200615...3146508594

%C .192.1083.18464..323306..5656712.100110527..1766745035..31272546310

%C .384.2210.48959.1109170.25396322.587134035.13518543301.312946900074

%H R. H. Hardin, <a href="/A275401/b275401.txt">Table of n, a(n) for n = 1..243</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) for n>3

%F k=2: [order 9] for n>10

%F k=3: [order 24] for n>28

%F k=4: [order 65] for n>69

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -3*a(n-2)

%F n=2: a(n) = 6*a(n-1) for n>2

%F n=3: a(n) = 4*a(n-1) +6*a(n-2) +4*a(n-3)

%F n=4: a(n) = 3*a(n-1) +11*a(n-2) +25*a(n-3) +2*a(n-4) -24*a(n-5) for n>6

%F n=5: [order 9] for n>10

%F n=6: [order 16] for n>17

%F n=7: [order 21] for n>22

%e Some solutions for n=4 k=4

%e ..0..1..1..1. .0..0..1..1. .0..0..0..1. .0..1..1..2. .0..1..0..0

%e ..2..2..0..1. .2..2..0..0. .1..2..2..0. .0..0..0..0. .0..2..1..1

%e ..1..2..2..2. .1..2..2..0. .1..1..1..2. .1..2..2..0. .1..2..2..1

%e ..1..0..1..2. .1..1..1..1. .0..0..0..1. .1..1..1..2. .1..1..0..0

%Y Column 1 is A003945(n-2).

%Y Row 1 is A007051(n-1).

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 26 2016