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A295716
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T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1, 2 or 4 1s.
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7
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2, 4, 4, 8, 16, 8, 16, 57, 57, 16, 32, 209, 385, 209, 32, 64, 768, 2580, 2580, 768, 64, 128, 2816, 17364, 31985, 17364, 2816, 128, 256, 10329, 116902, 396571, 396571, 116902, 10329, 256, 512, 37889, 786804, 4919857, 9056598, 4919857, 786804, 37889, 512
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OFFSET
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1,1
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COMMENTS
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Table starts
...2......4........8.........16............32..............64
...4.....16.......57........209...........768............2816
...8.....57......385.......2580.........17364..........116902
..16....209.....2580......31985........396571.........4919857
..32....768....17364.....396571.......9056598.......206899873
..64...2816...116902....4919857.....206899873......8705322572
.128..10329...786804...61023234....4725935539....366212961052
.256..37889..5295555..756896741..107948235688..15405701771951
.512.138980.35642190.9388238587.2465745246117.648089607011677
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5)
k=3: [order 12]
k=4: [order 28]
k=5: [order 76]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..0....0..0..1..1....0..1..0..0....0..0..1..1....0..1..0..1
..0..1..0..0....1..0..0..1....0..0..0..0....0..0..0..0....1..1..1..0
..1..0..1..1....0..0..1..0....1..0..1..1....0..0..1..1....0..1..0..1
..0..1..1..0....0..0..1..0....1..0..1..0....1..0..0..1....1..0..1..1
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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