A240629 - OEIS

%I #4 Apr 09 2014 18:30:45

%S 1,2,2,4,10,4,12,109,109,12,40,1332,4369,1332,40,143,16624,180480,

%T 180480,16624,143,528,208015,7462748,24648700,7462748,208015,528,1979,

%U 2604059,308596193,3367163455,3367163455,308596193,2604059,1979,7466,32601488

%N T(n,k)=Number of nXk 0..3 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..3 introduced in row major order

%C Table starts

%C ...1......2.........4...........12..............40.................143

%C ...2.....10.......109.........1332...........16624..............208015

%C ...4....109......4369.......180480.........7462748...........308596193

%C ..12...1332....180480.....24648700......3367163455........459961775083

%C ..40..16624...7462748...3367163455...1519699081714.....685854075788477

%C .143.208015.308596193.459961775083.685854075788477.1022628784514567961

%H R. H. Hardin, <a href="/A240629/b240629.txt">Table of n, a(n) for n = 1..83</a>

%F Empirical for column k:

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

%F k=2: [order 10] for n>11

%F k=3: [order 46]

%e Some solutions for n=3 k=4

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

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

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

%Y Column 1 is A204678

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 09 2014