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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
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 11 2018
STATUS
approved