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

Author

R. H. Hardin, Jan 07 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

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