A298970 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 219, 128, 16, 32, 512, 1575, 1575, 512, 32, 64, 2048, 11283, 21098, 11283, 2048, 64, 128, 8192, 80972, 280468, 280468, 80972, 8192, 128, 256, 32768, 581057, 3740381, 6892031, 3740381, 581057, 32768, 256, 512, 131072

Offset: 1

Author

R. H. Hardin, Jan 30 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1.....2.......4.........8...........16.............32...............64

...2.....8......32.......128..........512...........2048.............8192

...4....32.....219......1575........11283..........80972...........581057

...8...128....1575.....21098.......280468........3740381.........49885231

..16...512...11283....280468......6892031......170137416.......4200575252

..32..2048...80972...3740381....170137416.....7785598672.....356356552103

..64..8192..581057..49885231...4200575252...356356552103...30241030285680

.128.32768.4169867.665351771.103715870545.16312003284843.2566506415636896

Examples

			Some solutions for n=5 k=4
..0..0..0..1. .0..0..1..1. .0..0..0..1. .0..0..1..0. .0..0..0..0
..1..1..0..1. .0..0..0..0. .1..0..0..0. .1..1..1..0. .0..0..1..0
..0..1..0..1. .0..1..1..1. .1..1..0..1. .1..1..0..1. .0..1..1..0
..0..0..0..1. .1..1..0..1. .1..1..1..0. .1..0..0..0. .1..1..0..1
..0..1..1..0. .0..0..1..0. .0..0..0..1. .1..1..1..0. .1..0..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

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

k=3: [order 8]

k=4: [order 23]

k=5: [order 75]