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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 9 23:26 EDT 2020. Contains 336335 sequences. (Running on oeis4.)