A241119 T(n,k)=Number of nXk 0..3 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..3 introduced in row major order.

1, 2, 2, 5, 15, 5, 15, 178, 178, 15, 51, 2614, 9918, 2614, 51, 187, 40148, 587555, 587555, 40148, 187, 715, 622645, 35000157, 134229632, 35000157, 622645, 715, 2795, 9676364, 2085879115, 30679522712, 30679522712, 2085879115, 9676364, 2795

Offset: 1

Author

R. H. Hardin, Apr 16 2014

Keywords

• nonn
• tabl

Comments

Table starts

...1......2..........5............15................51..................187

...2.....15........178..........2614.............40148...............622645

...5....178.......9918........587555..........35000157...........2085879115

..15...2614.....587555.....134229632.......30679522712........7012241396116

..51..40148...35000157...30679522712....26891788727245....23571710809729613

.187.622645.2085879115.7012241396116.23571710809729613.79236581561126536192

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..84

Crossrefs

Column 1 is A007581(n-1)

Column 2 is A200795

Formula

Empirical for column k:

k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)

k=2: [order 8] for n>10

k=3: [order 20] for n>21

k=4: [order 74] for n>75