A253035 T(n,k) = Number of (n+2) X (k+2) 0..2 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order.

297, 1647, 1647, 9126, 12987, 9126, 50571, 102060, 102060, 50571, 280233, 802899, 1134864, 802899, 280233, 1552878, 6320511, 12647772, 12647772, 6320511, 1552878, 8605089, 49756086, 141199416, 199953846, 141199416, 49756086, 8605089

Offset

1,1

Comments

Table starts

.....297......1647........9126........50571.........280233..........1552878

....1647.....12987......102060.......802899........6320511.........49756086

....9126....102060.....1134864.....12647772......141199416.......1576282464

...50571....802899....12647772....199953846.....3170197872......50259172356

..280233...6320511...141199416...3170197872....71502727077....1612681662123

.1552878..49756086..1576282464..50259172356..1612681662123...51750105608403

.8605089.391717269.17600380920.797070583521.36393871038174.1662024911503707

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

k=1: a(n) = 5*a(n-1) +3*a(n-2),

k=2: a(n) = 9*a(n-1) -5*a(n-2) -10*a(n-3) -174*a(n-4) +80*a(n-5) +160*a(n-6),

k=3: [order 20],

k=4: [order 72].

Example

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

Crossrefs

Sequence in context: A053394 A179158 A037043 * A253029 A251289 A281132

Adjacent sequences: A253032 A253033 A253034 * A253036 A253037 A253038

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 26 2014

Status

approved