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A277767 T(n,k)=Number of nXk 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.

%I A277767 #4 Oct 29 2016 07:30:38
%S A277767 0,0,0,0,1,0,0,4,2,0,0,18,17,14,0,0,80,204,330,56,0,0,356,1989,9741,
%T A277767 3666,284,0,0,1584,21141,275018,270291,46289,1304,0,0,7048,220549,
%U A277767 7824415,20049229,8971150,560809,6248,0,0,31360,2292380,221983169,1487830718
%N A277767 T(n,k)=Number of nXk 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.
%C A277767 Table starts
%C A277767 .0......0..........0.............0.................0...................0
%C A277767 .0......1..........4............18................80.................356
%C A277767 .0......2.........17...........204..............1989...............21141
%C A277767 .0.....14........330..........9741............275018.............7824415
%C A277767 .0.....56.......3666........270291..........20049229..........1487830718
%C A277767 .0....284......46289.......8971150........1762881313........343944986355
%C A277767 .0...1304.....560809.....280603511......145416104585......74591651561541
%C A277767 .0...6248....6883464....8946059000....12253138042478...16513537201433122
%C A277767 .0..29408...84161576..283436060320..1025207978301185.3631417278822015869
%C A277767 .0.139472.1030163755.8998418743638.85977721285058269
%H A277767 R. H. Hardin, <a href="/A277767/b277767.txt">Table of n, a(n) for n = 1..112</a>
%F A277767 Empirical for column k:
%F A277767 k=2: a(n) = 4*a(n-1) +6*a(n-2) -12*a(n-3)
%F A277767 k=3: [order 11]
%F A277767 k=4: [order 44] for n>45
%F A277767 Empirical for row n:
%F A277767 n=2: a(n) = 4*a(n-1) +2*a(n-2)
%F A277767 n=3: [order 18]
%F A277767 n=4: [order 98]
%e A277767 Some solutions for n=4 k=4
%e A277767 ..0..1..2..0. .0..1..2..0. .0..1..2..0. .0..1..2..0. .0..1..2..0
%e A277767 ..2..1..1..1. .2..0..0..1. .2..2..0..1. .2..0..1..1. .2..2..1..1
%e A277767 ..2..0..2..0. .0..1..0..2. .1..0..0..1. .0..1..2..0. .1..0..2..0
%e A277767 ..1..2..1..0. .2..2..1..2. .2..1..2..2. .1..2..1..1. .2..0..1..2
%Y A277767 Row 2 is A090017(n-1).
%K A277767 nonn,tabl
%O A277767 1,8
%A A277767 _R. H. Hardin_, Oct 29 2016