A320371 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 228, 128, 16, 32, 512, 1612, 1612, 512, 32, 64, 2048, 11396, 19840, 11396, 2048, 64, 128, 8192, 80568, 245060, 245060, 80568, 8192, 128, 256, 32768, 569608, 3027408, 5304988, 3027408, 569608, 32768, 256, 512, 131072

Offset

1,2

Comments

Table starts

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

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

...4.....32......228.......1612.........11396...........80568............569608

...8....128.....1612......19840........245060.........3027408..........37398884

..16....512....11396.....245060.......5304988.......114844160........2486026176

..32...2048....80568....3027408.....114844160......4358279956......165355751224

..64...8192...569608...37398884....2486026176....165355751224....10993944343316

.128..32768..4027076..462004160...53815748216...6274017360108...731023916987668

.256.131072.28471056.5707334644.1164968680976.238053099337172.48608312646628816

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

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

k=3: a(n) = 8*a(n-1) -7*a(n-2) +3*a(n-3)

k=4: [order 9]

k=5: [order 25] for n>26

k=6: [order 70] for n>73

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A004171(n-1).

Sequence in context: A299740 A316815 A299661 * A317565 A302741 A300215

Adjacent sequences: A320368 A320369 A320370 * A320372 A320373 A320374

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 11 2018

Status

approved