A277767 - OEIS

%I #4 Oct 29 2016 07:30:38

%S 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 3666,284,0,0,1584,21141,275018,270291,46289,1304,0,0,7048,220549,

%U 7824415,20049229,8971150,560809,6248,0,0,31360,2292380,221983169,1487830718

%N 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 Table starts

%C .0......0..........0.............0.................0...................0

%C .0......1..........4............18................80.................356

%C .0......2.........17...........204..............1989...............21141

%C .0.....14........330..........9741............275018.............7824415

%C .0.....56.......3666........270291..........20049229..........1487830718

%C .0....284......46289.......8971150........1762881313........343944986355

%C .0...1304.....560809.....280603511......145416104585......74591651561541

%C .0...6248....6883464....8946059000....12253138042478...16513537201433122

%C .0..29408...84161576..283436060320..1025207978301185.3631417278822015869

%C .0.139472.1030163755.8998418743638.85977721285058269

%H R. H. Hardin, <a href="/A277767/b277767.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=2: a(n) = 4*a(n-1) +6*a(n-2) -12*a(n-3)

%F k=3: [order 11]

%F k=4: [order 44] for n>45

%F Empirical for row n:

%F n=2: a(n) = 4*a(n-1) +2*a(n-2)

%F n=3: [order 18]

%F n=4: [order 98]

%e Some solutions for n=4 k=4

%e ..0..1..2..0. .0..1..2..0. .0..1..2..0. .0..1..2..0. .0..1..2..0

%e ..2..1..1..1. .2..0..0..1. .2..2..0..1. .2..0..1..1. .2..2..1..1

%e ..2..0..2..0. .0..1..0..2. .1..0..0..1. .0..1..2..0. .1..0..2..0

%e ..1..2..1..0. .2..2..1..2. .2..1..2..2. .1..2..1..1. .2..0..1..2

%Y Row 2 is A090017(n-1).

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Oct 29 2016