A297876 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 5 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 0, 2, 0, 0, 11, 3, 3, 11, 0, 0, 13, 0, 10, 0, 13, 0, 0, 34, 3, 20, 20, 3, 34, 0, 0, 65, 6, 68, 80, 68, 6, 65, 0, 0, 123, 23, 185, 231, 231, 185, 23, 123, 0, 0, 266, 68, 561, 579, 887, 579, 561, 68, 266, 0, 0, 499, 205, 1588, 2437, 3307, 3307, 2437

Offset

1,8

Comments

Table starts

.0...0..0....0....0.....0......0.......0........0.........0.........0

.0...1..3....2...11....13.....34......65......123.......266.......499

.0...3..0....3....0.....3......6......23.......68.......205.......572

.0...2..3...10...20....68....185.....561.....1588......4814.....14322

.0..11..0...20...80...231....579....2437.....7507.....26278.....91622

.0..13..3...68..231...887...3307...13910....55501....228947....947582

.0..34..6..185..579..3307..13778...69160...325394...1617897...7900112

.0..65.23..561.2437.13910..69160..428609..2364407..14043631..81562636

.0.123.68.1588.7507.55501.325394.2364407.15589226.109627764.757954739

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

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

k=3: [order 17] for n>18

k=4: [order 52] for n>53

Example

Some solutions for n=7 k=4
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..0..1..0..1. .0..1..1..0. .1..0..1..0. .0..0..0..0. .0..0..0..0
..0..1..1..0. .1..0..1..0. .1..1..0..0. .1..1..1..1. .1..1..1..1
..0..1..0..1. .1..0..0..1. .1..0..1..0. .1..0..0..1. .1..0..0..1
..0..1..0..1. .1..1..1..1. .1..0..0..1. .0..1..0..1. .0..0..1..0
..0..1..0..1. .0..0..0..0. .1..0..1..0. .0..1..1..0. .1..0..0..1
..0..0..1..1. .0..0..0..0. .1..1..0..0. .0..0..0..0. .1..1..1..1

Crossrefs

Sequence in context: A287712 A287784 A325010 * A298139 A298087 A298259

Adjacent sequences: A297873 A297874 A297875 * A297877 A297878 A297879

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 07 2018

Status

approved