A299661 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 227, 128, 16, 32, 512, 1642, 1642, 512, 32, 64, 2048, 11888, 22087, 11888, 2048, 64, 128, 8192, 86123, 297071, 297071, 86123, 8192, 128, 256, 32768, 624007, 4001253, 7411398, 4001253, 624007, 32768, 256, 512, 131072

Offset: 1

Author

R. H. Hardin, Feb 15 2018

Keywords

• nonn
• tabl

Comments

Table starts

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

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

...4.....32......227.......1642.........11888...........86123

...8....128.....1642......22087........297071.........4001253

..16....512....11888.....297071.......7411398.......185302633

..32...2048....86123....4001253.....185302633......8607101770

..64...8192...624007...53909088....4634931975....400012077773

.128..32768..4521433..726363190..115940148451..18591844096646

.256.131072.32761769.9787119222.2900256951630.864147943636240

Examples

			Some solutions for n=5 k=5
..0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0. .0..0..0..0..0
..0..0..0..0..0. .0..0..1..1..0. .0..0..1..1..0. .0..1..0..0..0
..1..0..0..1..0. .1..1..1..1..0. .0..0..0..1..0. .0..0..1..1..1
..1..1..0..1..0. .1..1..0..0..0. .0..1..1..1..1. .0..1..1..0..0
..1..1..0..1..1. .0..0..0..1..0. .0..0..0..1..0. .0..0..1..1..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 24]

k=5: [order 89]