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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A316960 A299740 A316815 * A320371 A317565 A302741

Adjacent sequences: A299658 A299659 A299660 * A299662 A299663 A299664

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 15 2018

Status

approved