A298139 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 7 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, 88, 68, 6, 65, 0, 0, 123, 23, 185, 242, 242, 185, 23, 123, 0, 0, 266, 68, 561, 627, 917, 627, 561, 68, 266, 0, 0, 499, 205, 1600, 2604, 3417, 3417, 2604

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.....1600......4856.....14490

.0..11..0...20...88...242....627....2604.....8137.....28727....101137

.0..13..3...68..242...917...3417...14533....58845....244155...1024766

.0..34..6..185..627..3417..14422...73961...354200...1772595...8807624

.0..65.23..561.2604.14533..73961..467043..2633905..15796516..93682029

.0.123.68.1600.8137.58845.354200.2633905.17828062.127068717.899366629

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 60] for n>61

Example

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

Crossrefs

Column 2 is A297870.

Column 3 is A297871.

Sequence in context: A287784 A325010 A297876 * A298087 A298259 A298930

Adjacent sequences: A298136 A298137 A298138 * A298140 A298141 A298142

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 13 2018

Status

approved