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%I #4 Dec 01 2014 19:33:03
%S 85,455,455,2450,3315,2450,13275,24714,24714,13275,72375,189129,
%T 263824,189129,72375,397000,1487375,3014066,3014066,1487375,397000,
%U 2190625,12022920,36988354,55048995,36988354,12022920,2190625,12156875,99776859
%N T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with every 2X2 subblock summing to a nonzero multiple of 3
%C Table starts
%C ......85......455.......2450........13275..........72375............397000
%C .....455.....3315......24714.......189129........1487375..........12022920
%C ....2450....24714.....263824......3014066.......36988354.........486098916
%C ...13275...189129....3014066.....55048995.....1151715397.......27005232676
%C ...72375..1487375...36988354...1151715397....43807665267.....1921884757552
%C ..397000.12022920..486098916..27005232676..1921884757552...159630812543048
%C .2190625.99776859.6775415354.687109914883.91970680872031.14450351430729220
%H R. H. Hardin, <a href="/A251343/b251343.txt">Table of n, a(n) for n = 1..143</a>
%F Empirical for column k:
%F k=1: a(n) = 10*a(n-1) -20*a(n-2) -25*a(n-3)
%F k=2: [order 7]
%F k=3: [order 17]
%F k=4: [order 41]
%e Some solutions for n=2 k=4
%e ..2..2..2..0..1....1..0..0..3..3....2..3..0..3..1....1..0..2..1..0
%e ..0..2..0..1..1....3..2..1..2..1....1..0..0..0..2....2..0..1..2..0
%e ..2..2..2..3..1....1..3..0..3..0....2..0..3..0..1....1..3..2..1..3
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
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