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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A007581(n-1)

Column 2 is A200795

Sequence in context: A208353 A208001 A200801 * A208408 A198528 A208466

Adjacent sequences: A241116 A241117 A241118 * A241120 A241121 A241122

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 16 2014

Status

approved