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A301491
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T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 2, 4, 5 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, 7, 4, 8, 18, 18, 8, 16, 50, 52, 50, 16, 32, 138, 148, 148, 138, 32, 64, 383, 441, 599, 441, 383, 64, 128, 1063, 1372, 2354, 2354, 1372, 1063, 128, 256, 2951, 4326, 9415, 15124, 9415, 4326, 2951, 256, 512, 8193, 13641, 38558, 93753, 93753, 38558, 13641
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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
...2....7....18.....50......138.......383........1063.........2951
...4...18....52....148......441......1372........4326........13641
...8...50...148....599.....2354......9415.......38558.......158994
..16..138...441...2354....15124.....93753......594953......3838256
..32..383..1372...9415....93753....903707.....8479276.....81180752
..64.1063..4326..38558...594953...8479276...116648010...1642511178
.128.2951.13641.158994..3838256..81180752..1642511178..34593556316
.256.8193.42741.657238.24838061.782053062.23269383762.732289348979
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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) +a(n-3) +a(n-4) -2*a(n-5) -a(n-6),
k=3: [order 24] for n>25,
k=4: [order 89] for n>91.
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EXAMPLE
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Some solutions for n=5, k=4
..0..1..0..0. .0..1..1..1. .0..0..1..1. .0..0..1..0. .0..1..1..0
..1..0..1..0. .1..0..0..1. .0..1..0..1. .1..0..0..0. .0..1..0..0
..0..1..1..1. .0..1..0..1. .1..0..1..0. .1..1..0..0. .0..0..0..0
..1..1..0..0. .0..1..0..0. .1..0..1..0. .0..1..0..0. .1..0..0..0
..0..1..1..0. .0..1..1..0. .1..0..0..1. .1..0..1..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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