A277788 - OEIS

%I #4 Oct 31 2016 12:54:13

%S 0,0,0,0,3,0,0,12,12,0,0,84,80,84,0,0,498,1434,1434,498,0,0,3090,

%T 20663,79092,20663,3090,0,0,18930,309612,3182256,3182256,309612,18930,

%U 0,0,116382,4604554,137510661,352957610,137510661,4604554,116382,0,0,714810

%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) (1,-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......3.........12.............84...............498..................3090

%C .0.....12.........80...........1434.............20663................309612

%C .0.....84.......1434..........79092...........3182256.............137510661

%C .0....498......20663........3182256.........352957610...........42007318111

%C .0...3090.....309612......137510661.......42007318111........13899171401510

%C .0..18930....4604554.....5841628899.....4917756016412......4515609963711003

%C .0.116382...68632481...249237125709...578187054139243...1473737617518590407

%C .0.714810.1022176517.10621140577245.67894823921434433.480374435720722263006

%H R. H. Hardin, <a href="/A277788/b277788.txt">Table of n, a(n) for n = 1..112</a>

%F Empirical for column k:

%F k=2: a(n) = 5*a(n-1) +8*a(n-2) -6*a(n-3)

%F k=3: [order 23] for n>24

%F k=4: [order 48] for n>50

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Oct 31 2016