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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A204678

Sequence in context: A295416 A202802 A059473 * A360313 A162508 A199400

Adjacent sequences: A240626 A240627 A240628 * A240630 A240631 A240632

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 09 2014

Status

approved