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A304775
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T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 7 king-move adjacent elements, with upper left element zero.
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7
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1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 27, 49, 16, 32, 120, 67, 67, 120, 32, 64, 293, 139, 172, 139, 293, 64, 128, 719, 303, 443, 443, 303, 719, 128, 256, 1774, 685, 1094, 1581, 1094, 685, 1774, 256, 512, 4389, 1511, 2710, 5060, 5060, 2710, 1511, 4389, 512, 1024, 10893
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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
...2....8...21....49....120.....293......719......1774.......4389.......10893
...4...21...27....67....139.....303......685......1511.......3316........7349
...8...49...67...172....443....1094.....2710......6861......17205.......43090
..16..120..139...443...1581....5060....15349.....50030.....160513......515542
..32..293..303..1094...5060...23872...100581....453229....2074725.....9305892
..64..719..685..2710..15349..100581...540901...3257711...19908669...116435693
.128.1774.1511..6861..50030..453229..3257711..26814986..224727491..1800071431
.256.4389.3316.17205.160513.2074725.19908669.224727491.2642187354.28890049643
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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) +a(n-2) -4*a(n-3) -4*a(n-4) for n>5
k=3: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) for n>8
k=4: [order 10] for n>13
k=5: [order 25] for n>28
k=6: [order 46] for n>50
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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..1..1..1. .0..1..1..0. .0..0..0..1
..0..0..0..0. .0..0..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1
..0..0..1..0. .1..1..1..1. .1..0..0..1. .1..0..0..1. .0..1..1..1
..0..0..1..0. .1..1..1..1. .1..1..1..1. .1..1..1..1. .1..1..1..0
..1..0..0..0. .1..1..1..0. .1..1..1..0. .1..1..1..1. .0..1..0..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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