%I #4 Nov 15 2013 14:27:52

%S 4,4,16,16,84,64,50,668,318,256,144,5070,8426,1328,1024,422,42104,

%T 206808,152180,6064,4096,1268,326010,4736026,11159202,2462572,26918,

%U 16384,3823,2511252,94464137,691418144,518972238,36885538,116909,65536,11472

%N T(n,k)=Number of nXk 0..3 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors

%C Table starts

%C .......4.......4............16...............50................144

%C ......16......84...........668.............5070..............42104

%C ......64.....318..........8426...........206808............4736026

%C .....256....1328........152180.........11159202..........691418144

%C ....1024....6064.......2462572........518972238........86074040354

%C ....4096...26918......36885538......23280281589.....10417626293694

%C ...16384..116909.....586971925....1098832065447...1320620287047433

%C ...65536..511264....9394148948...52087504055935.167980047970274816

%C ..262144.2248196..147360195020.2432351670277323

%C .1048576.9868600.2323912599668

%H R. H. Hardin, <a href="/A231940/b231940.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

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

%F k=2: [order 19] for n>20

%F k=3: [order 65] for n>66

%F Empirical for row n:

%F n=1: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7) for n>8

%F n=2: [order 15]

%e Some solutions for n=3 k=4

%e ..0..0..0..1....0..0..0..3....2..0..0..2....0..2..2..1....0..0..1..0

%e ..2..0..2..2....3..0..0..3....3..3..0..0....3..0..0..2....2..0..0..3

%e ..2..3..0..0....1..2..3..0....1..0..0..2....2..0..0..0....0..2..3..2

%Y Column 1 is A000302

%Y Column 2 is A231741

%Y Row 1 is A203094 for n>1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 15 2013