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A301443
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 32, 32, 8, 16, 128, 232, 128, 16, 32, 512, 1708, 1708, 512, 32, 64, 2048, 12576, 23672, 12576, 2048, 64, 128, 8192, 92616, 327848, 327848, 92616, 8192, 128, 256, 32768, 682084, 4543028, 8525992, 4543028, 682084, 32768, 256, 512, 131072
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OFFSET
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1,2
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COMMENTS
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Table starts
...1......2........4...........8............16...............32
...2......8.......32.........128...........512.............2048
...4.....32......232........1708.........12576............92616
...8....128.....1708.......23672........327848..........4543028
..16....512....12576......327848.......8525992........221935656
..32...2048....92616.....4543028.....221935656......10857946336
..64...8192...682084....62956480....5777358820.....531234388944
.128..32768..5023328...872451104..150397035552...25991845818768
.256.131072.36995208.12090455460.3915165237488.1271713349901092
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..286
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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) = 4*a(n-1)
k=3: a(n) = 8*a(n-1) -4*a(n-2) -5*a(n-3)
k=4: [order 11]
k=5: [order 31]
k=6: [order 97] for n>98
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EXAMPLE
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Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
..0..0..1..0. .0..1..1..1. .0..1..0..1. .0..1..0..1. .0..0..1..0
..1..0..1..0. .0..0..1..1. .0..1..1..1. .1..1..0..1. .1..1..1..0
..1..0..1..0. .1..0..0..0. .1..0..0..1. .0..1..0..1. .1..0..0..0
..1..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..0
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CROSSREFS
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Column 1 is A000079(n-1).
Column 2 is A004171(n-1).
Sequence in context: A300215 A300804 A303456 * A302010 A301784 A316808
Adjacent sequences: A301440 A301441 A301442 * A301444 A301445 A301446
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Mar 21 2018
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STATUS
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approved
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