A300215 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 228, 128, 16, 32, 512, 1651, 1651, 512, 32, 64, 2048, 11965, 22194, 11965, 2048, 64, 128, 8192, 86775, 298600, 298600, 86775, 8192, 128, 256, 32768, 629440, 4023881, 7452385, 4023881, 629440, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......228.......1651.........11965...........86775

...8....128.....1651......22194........298600.........4023881

..16....512....11965.....298600.......7452385.......186427449

..32...2048....86775....4023881.....186427449......8664017314

..64...8192...629440...54246856....4666136435....402932952786

.128..32768..4566023..731384148..116802113451..18741286700978

.256.131072.33122989.9861234001.2923892905217.871742323938453

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=4
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..0
..0..1..0..1. .0..0..1..1. .1..1..1..1. .1..1..0..1. .0..1..0..0
..0..0..1..0. .1..0..1..0. .1..0..1..1. .1..1..0..1. .1..1..1..0
..0..1..1..0. .0..0..1..0. .0..0..0..0. .0..0..0..1. .0..1..1..1
..0..0..1..1. .0..0..0..0. .0..0..1..0. .1..0..0..0. .0..0..1..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A320371 A317565 A302741 * A300804 A303456 A301443

Adjacent sequences: A300212 A300213 A300214 * A300216 A300217 A300218

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 28 2018

Status

approved