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A230940
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T(n,k)=Number of white-square subarrays of (n+2)X(k+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero
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5
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0, 2, 2, 2, 6, 2, 8, 16, 16, 8, 8, 48, 34, 48, 8, 42, 146, 232, 232, 146, 42, 42, 438, 522, 1242, 522, 438, 42, 208, 1312, 3768, 6896, 6896, 3768, 1312, 208, 208, 3936, 8450, 37984, 28216, 37984, 8450, 3936, 208, 1042, 11810, 60824, 208172, 396950, 396950
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OFFSET
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1,2
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COMMENTS
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Table starts
...0....2.....2.......8........8........42.........42..........208
...2....6....16......48......146.......438.......1312.........3936
...2...16....34.....232......522......3768.......8450........60824
...8...48...232....1242.....6896.....37984.....208172......1142054
...8..146...522....6896....28216....396950....1604098.....22368688
..42..438..3768...37984...396950...4092246...41991510....431437274
..42.1312..8450..208172..1604098..41991510..318984080...8279222070
.208.3936.60824.1142054.22368688.431437274.8279222070.159130979900
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-2) +5*a(n-4)
k=2: a(n) = 3*a(n-1) -a(n-2) +3*a(n-3)
k=3: a(n) = 16*a(n-2) +3*a(n-4) -10*a(n-6) +24*a(n-8) -16*a(n-10)
k=4: [order 17]
k=5: [order 44]
k=6: [order 71]
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EXAMPLE
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Some solutions for n=4 k=4
..0..x..0..x..0..x....0..x..0..x..3..x....0..x..0..x..2..x....0..x..0..x..0..x
..x..1..x..3..x..1....x..1..x..2..x..0....x..1..x..3..x..1....x..1..x..1..x..3
..2..x..0..x..2..x....2..x..0..x..1..x....2..x..2..x..0..x....2..x..2..x..0..x
..x..3..x..3..x..3....x..3..x..3..x..3....x..3..x..1..x..3....x..3..x..3..x..3
..2..x..2..x..0..x....2..x..2..x..0..x....2..x..0..x..2..x....0..x..2..x..0..x
..x..1..x..1..x..3....x..1..x..1..x..3....x..3..x..1..x..1....x..1..x..1..x..3
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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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