A231080 - OEIS

%I #4 Nov 03 2013 10:54:31

%S 0,0,0,0,2,0,0,14,2,0,0,40,50,16,0,0,356,136,784,34,0,0,1840,2820,

%T 6400,5098,154,0,0,10128,38000,523936,71944,54426,432,0,0,60808,

%U 421920,18937480,18655220,1866192,441392,1618,0,0,337016,6118120,696453136

%N T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero

%C Table starts

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

%C .0....2......14........40...........356...........1840...........10128

%C .0....2......50.......136..........2820..........38000..........421920

%C .0...16.....784......6400........523936.......18937480.......696453136

%C .0...34....5098.....71944......18655220.....1782634608....190102522528

%C .0..154...54426...1866192....1480839364...417868659864.131563996224512

%C .0..432..441392..32292680...79624748768.61990953794520

%C .0.1618.4164402.679262904.5187293040908

%H R. H. Hardin, <a href="/A231080/b231080.txt">Table of n, a(n) for n = 1..83</a>

%F Empirical for column k:

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

%F k=3: [order 11]

%F k=4: [order 36]

%F Empirical for row n:

%F n=2: a(n) = 3*a(n-1) +12*a(n-2) +30*a(n-3) -64*a(n-4) +16*a(n-5)

%F n=3: [order 35]

%e Some solutions for n=3 k=4

%e ..0..1..2..3....0..3..2..1....0..1..0..3....0..1..0..1....0..3..0..3

%e ..2..3..0..3....2..1..0..1....0..3..2..3....2..3..2..3....0..1..2..3

%e ..2..1..2..1....2..3..2..1....2..1..0..3....2..1..0..1....0..3..0..1

%Y Column 2 is A230800

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 03 2013