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%I #4 Nov 01 2013 18:46:46
%S 0,2,2,2,6,2,8,16,16,8,8,48,34,48,8,42,146,232,232,146,42,42,438,522,
%T 1242,522,438,42,208,1312,3768,6896,6896,3768,1312,208,208,3936,8450,
%U 37984,28216,37984,8450,3936,208,1042,11810,60824,208172,396950,396950
%N T(n,k)=Number of white-square subarrays of (n+2)X(k+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero
%C Table starts
%C ...0....2.....2.......8........8........42.........42..........208
%C ...2....6....16......48......146.......438.......1312.........3936
%C ...2...16....34.....232......522......3768.......8450........60824
%C ...8...48...232....1242.....6896.....37984.....208172......1142054
%C ...8..146...522....6896....28216....396950....1604098.....22368688
%C ..42..438..3768...37984...396950...4092246...41991510....431437274
%C ..42.1312..8450..208172..1604098..41991510..318984080...8279222070
%C .208.3936.60824.1142054.22368688.431437274.8279222070.159130979900
%H R. H. Hardin, <a href="/A230940/b230940.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-2) +5*a(n-4)
%F k=2: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3)
%F k=3: a(n) = 16*a(n-2) +3*a(n-4) -10*a(n-6) +24*a(n-8) -16*a(n-10)
%F k=4: [order 17]
%F k=5: [order 44]
%F k=6: [order 71]
%e Some solutions for n=4 k=4
%e ..0..x..0..x..0..x....0..x..0..x..3..x....0..x..0..x..2..x....0..x..0..x..0..x
%e ..x..1..x..3..x..1....x..1..x..2..x..0....x..1..x..3..x..1....x..1..x..1..x..3
%e ..2..x..0..x..2..x....2..x..0..x..1..x....2..x..2..x..0..x....2..x..2..x..0..x
%e ..x..3..x..3..x..3....x..3..x..3..x..3....x..3..x..1..x..3....x..3..x..3..x..3
%e ..2..x..2..x..0..x....2..x..2..x..0..x....2..x..0..x..2..x....0..x..2..x..0..x
%e ..x..1..x..1..x..3....x..1..x..1..x..3....x..3..x..1..x..1....x..1..x..1..x..3
%Y Column 1 is A230928
%Y Column 2 is A230929
%Y Column 4 is A230931
%Y Column 6 is A230933
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Nov 01 2013