A240629 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.

1, 2, 2, 4, 10, 4, 12, 109, 109, 12, 40, 1332, 4369, 1332, 40, 143, 16624, 180480, 180480, 16624, 143, 528, 208015, 7462748, 24648700, 7462748, 208015, 528, 1979, 2604059, 308596193, 3367163455, 3367163455, 308596193, 2604059, 1979, 7466, 32601488

Offset: 1

Author

R. H. Hardin, Apr 09 2014

Keywords

• nonn
• tabl

Comments

Table starts

...1......2.........4...........12..............40.................143

...2.....10.......109.........1332...........16624..............208015

...4....109......4369.......180480.........7462748...........308596193

..12...1332....180480.....24648700......3367163455........459961775083

..40..16624...7462748...3367163455...1519699081714.....685854075788477

.143.208015.308596193.459961775083.685854075788477.1022628784514567961

Examples

			Some solutions for n=3 k=4
..0..1..0..2....0..1..1..2....0..1..1..2....0..1..0..2....0..1..0..0
..3..0..3..0....3..0..3..2....1..2..3..0....3..3..2..1....0..2..1..2
..1..2..2..3....3..2..0..1....2..3..2..2....1..1..3..0....2..1..2..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..83

Crossrefs

Column 1 is A204678

Formula

Empirical for column k:

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

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

k=3: [order 46]