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A303800
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T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 2 or 4 king-move adjacent elements, with upper left element zero.
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8
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1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 17, 24, 16, 32, 64, 30, 30, 64, 32, 64, 184, 70, 90, 70, 184, 64, 128, 432, 121, 231, 231, 121, 432, 128, 256, 1088, 221, 631, 562, 631, 221, 1088, 256, 512, 2944, 421, 1586, 1406, 1406, 1586, 421, 2944, 512, 1024, 7360, 800
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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....64....128....256.....512....1024.....2048
...2....4..12....24....64....184...432...1088...2944....7360...18496....48384
...4...12..17....30....70....121...221....421....800....1511....2832.....5340
...8...24..30....90...231....631..1586...4230..11059...29053...75910...199512
..16...64..70...231...562...1406..2829...7014..16337...38826...88805...212475
..32..184.121...631..1406...5282.11733..41444.108170..344248..929630..2892458
..64..432.221..1586..2829..11733.15478..67090..96021..421513..602782..2643954
.128.1088.421..4230..7014..41444.67090.394667.764127.3928166.8156073.39226935
.256.2944.800.11059.16337.108170.96021.764127.587035.6174082.3728099.50846990
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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) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6
k=3: a(n) = a(n-1) +a(n-2) +2*a(n-3) -a(n-5) -2*a(n-6) -2*a(n-7) for n>10
k=4: [order 28] for n>32
k=5: [order 18] for n>24
k=6: [order 71] for n>75
k=7: [order 63] for n>71
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EXAMPLE
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Some solutions for n=5, k=4
..0..0..1..1. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0
..0..0..0..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..0
..1..0..0..0. .1..0..1..1. .1..1..1..0. .0..0..0..0. .0..0..0..0
..0..1..0..1. .0..1..1..1. .0..1..0..1. .0..0..0..1. .0..0..0..1
..1..1..1..0. .1..1..1..1. .1..0..0..0. .0..0..1..0. .0..0..1..0
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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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