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A296554
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T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.
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6
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 4, 5, 4, 1, 1, 1, 1, 5, 7, 7, 5, 1, 1, 1, 1, 7, 10, 11, 10, 7, 1, 1, 1, 1, 10, 17, 18, 18, 17, 10, 1, 1, 1, 1, 14, 28, 34, 32, 34, 28, 14, 1, 1, 1, 1, 19, 43, 59, 62, 62, 59, 43, 19, 1, 1, 1, 1, 26, 66, 100, 118, 148, 118, 100, 66, 26
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OFFSET
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1,13
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COMMENTS
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Table starts
.1.1..1..1...1...1...1....1....1.....1.....1......1......1.......1.......1
.1.1..1..1...1...1...1....1....1.....1.....1......1......1.......1.......1
.1.1..2..3...4...5...7...10...14....19....26.....36.....50......69......95
.1.1..3..5...7..10..17...28...43....66...105....168....264.....413.....651
.1.1..4..7..11..18..34...59..100...174...309....538....930....1620....2835
.1.1..5.10..18..32..62..118..227...439...839...1592...3037....5823...11144
.1.1..7.17..34..62.148..347..786..1702..3761...8400..18843...41959...93233
.1.1.10.28..59.118.347..960.2418..5862.15035..39090.100159..253642..646112
.1.1.14.43.100.227.786.2418.6802.18758.55226.162010.467274.1341081.3887275
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1)
k=3: a(n) = a(n-1) +a(n-4)
k=4: a(n) = a(n-1) +2*a(n-4) +a(n-7)
k=5: a(n) = a(n-1) +3*a(n-4) +a(n-6) +3*a(n-7) +a(n-10)
k=6: a(n) = a(n-1) +4*a(n-4) +a(n-5) +3*a(n-6) +6*a(n-7) +2*a(n-9) +4*a(n-10) +a(n-13)
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EXAMPLE
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Some solutions for n=7 k=4
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1
..0..0..0..0. .0..1..1..1. .0..0..0..0. .0..1..1..0. .0..1..1..1
..0..0..0..0. .0..1..1..0. .0..0..0..0. .1..1..1..0. .0..1..1..0
..0..0..0..0. .0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0
..0..1..1..0. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..1..1..0
..1..1..1..0. .0..1..1..1. .0..1..1..0. .0..1..1..1. .1..1..1..0
..1..1..0..0. .0..1..1..0. .0..0..0..0. .0..1..1..0. .1..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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