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%I #4 Jan 19 2014 12:53:41
%S 14,69,69,358,417,358,1844,2688,2688,1844,9522,17406,24428,17406,9522,
%T 49108,112830,225216,225216,112830,49108,253476,731610,2085288,
%U 3024540,2085288,731610,253476,1307604,4743680,19292888,40825266,40825266
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays colored with the sets of distinct values in every 2X2 subblock, with new values 0..2 introduced row-major order
%C Table starts
%C .......14.........69..........358...........1844.............9522
%C .......69........417.........2688..........17406...........112830
%C ......358.......2688........24428.........225216..........2085288
%C .....1844......17406.......225216........3024540.........40825266
%C .....9522.....112830......2085288.......40825266........808607717
%C ....49108.....731610.....19292888......552336576......16045542980
%C ...253476....4743680....178764936.....7474034016.....318968276357
%C ..1307604...30758256...1654241464...101151676976....6333468781482
%C ..6748036..199437026..15328190976..1368939009490..125923500067477
%C .34815556.1293154716.141847742984.18526939344118.2500354560114878
%H R. H. Hardin, <a href="/A236164/b236164.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +18*a(n-2) +16*a(n-3) +12*a(n-4) -12*a(n-5) for n>6
%F k=2: [order 8]
%F k=3: [order 23] for n>26
%F k=4: [order 62] for n>66
%e Some solutions for n=3 k=4
%e ..0..0..1..1..0....0..0..0..1..0....0..0..0..1..2....0..0..0..1..2
%e ..0..2..1..2..2....0..0..2..1..1....0..0..2..1..2....0..2..1..1..0
%e ..1..1..2..0..2....2..0..1..1..1....1..1..2..2..0....1..1..2..0..1
%e ..2..2..0..0..1....2..1..1..1..2....1..1..2..2..2....2..1..0..2..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 19 2014
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