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A303314
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T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
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12
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1, 2, 2, 3, 3, 4, 5, 3, 4, 8, 8, 5, 12, 6, 16, 13, 7, 17, 11, 9, 32, 21, 13, 24, 36, 19, 14, 64, 34, 23, 67, 50, 74, 34, 22, 128, 55, 37, 158, 128, 139, 165, 53, 35, 256, 89, 63, 298, 439, 410, 349, 361, 83, 56, 512, 144, 109, 595, 1085, 1799, 1221, 853, 783, 136, 90, 1024, 233
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OFFSET
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1,2
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COMMENTS
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Table starts
...1..2...3....5....8....13.....21......34.......55........89........144
...2..3...3....5....7....13.....23......37.......63.......109........183
...4..4..12...17...24....67....158.....298......595......1337.......2863
...8..6..11...36...50...128....439....1085.....2431......6452......17455
..16..9..19...74..139...410...1799....5907....16494.....53290.....184915
..32.14..34..165..349..1221...7096...30280...102683....403872....1783894
..64.22..53..361..853..3453..26184..148313...618149...2955145...16591424
.128.35..83..783.2180.10223.100128..746323..3851318..22515378..159560449
.256.56.136.1710.5525.30247.387892.3784002.23967605.171306353.1539204838
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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) -a(n-3)
k=3: a(n) = a(n-1) +a(n-3) +a(n-4) for n>7
k=4: a(n) = a(n-1) +a(n-2) +3*a(n-3) +2*a(n-4) -a(n-5) -2*a(n-6) -a(n-7) for n>10
k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) +4*a(n-5) -10*a(n-6) -6*a(n-7) +4*a(n-9) for n>12
k=6: [order 8] for n>11
k=7: [order 20] for n>23
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +2*a(n-3) for n>5
n=3: a(n) = a(n-1) +3*a(n-3) +4*a(n-4) for n>7
n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +9*a(n-4) -3*a(n-5) -7*a(n-6) -2*a(n-7) for n>11
n=5: [order 12] for n>16
n=6: [order 23] for n>28
n=7: [order 46] for n>51
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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..0..1. .0..1..0..0. .0..1..0..1
..0..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..1. .0..1..1..1
..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1
..0..0..0..1. .0..0..0..1. .1..1..0..1. .0..1..0..1. .0..1..0..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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