%I #4 Oct 31 2013 05:42:32
%S 0,0,0,0,2,0,0,22,22,0,0,162,656,162,0,0,1202,16496,16496,1202,0,0,
%T 8974,416540,1361842,416540,8974,0,0,66990,10550264,114297392,
%U 114297392,10550264,66990,0,0,500018,267165468,9617769208,32002769030,9617769208
%N T(n,k)=Number of nXk 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero
%C Table starts
%C .0......0..........0..............0..................0......................0
%C .0......2.........22............162...............1202...................8974
%C .0.....22........656..........16496.............416540...............10550264
%C .0....162......16496........1361842..........114297392.............9617769208
%C .0...1202.....416540......114297392........32002769030..........8988055879558
%C .0...8974...10550264.....9617769208......8988055879558.......8428081775041778
%C .0..66990..267165468...809092017194...2523446670940914....7899599586975791528
%C .0.500018.6765343878.68064007019810.708459022763836116.7404104956669952823022
%H R. H. Hardin, <a href="/A230840/b230840.txt">Table of n, a(n) for n = 1..97</a>
%F Empirical for column k:
%F k=2: a(n) = 8*a(n-1) -5*a(n-2) +8*a(n-3) -4*a(n-4)
%F k=3: [order 30] for n>31
%e Some solutions for n=3 k=4
%e ..0..1..3..2....0..1..3..1....0..1..0..0....0..0..2..1....0..0..2..1
%e ..0..2..0..3....3..2..0..2....3..2..2..1....1..0..3..2....1..2..3..2
%e ..0..1..0..2....2..2..3..1....1..0..3..0....2..3..2..1....3..0..1..0
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Oct 31 2013