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A240321
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T(n,k)=Number of nXk 0..3 arrays with no element equal to two plus the sum of elements to its left or two plus the sum of the elements above it or zero plus the sum of the elements diagonally to its northwest, modulo 4
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6
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2, 2, 2, 4, 4, 4, 4, 18, 18, 4, 8, 44, 172, 44, 8, 8, 184, 866, 866, 184, 8, 16, 444, 7326, 8456, 7326, 444, 16, 16, 1826, 35042, 143682, 143682, 35042, 1826, 16, 32, 4388, 291982, 1352558, 4934092, 1352558, 291982, 4388, 32, 32, 18022, 1387224, 22643786
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OFFSET
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1,1
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COMMENTS
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Table starts
..2.....2........4...........4..............8...............8...............16
..2.....4.......18..........44............184.............444.............1826
..4....18......172.........866...........7326...........35042...........291982
..4....44......866........8456.........143682.........1352558.........22643786
..8...184.....7326......143682........4934092........92600224.......3120733284
..8...444....35042.....1352558.......92600224......3462370700.....233738937688
.16..1826...291982....22643786.....3120733284....233738937688...31675283550406
.16..4388..1387224...211572262....58052954898...8672268288766.2350783897073214
.32.18022.11520638..3529400774..1946100075968.582902538705858
.32.43300.54650290.32917918872.36103692985126
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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-2)
k=2: a(n) = 12*a(n-2) -24*a(n-4) +31*a(n-6) -16*a(n-8)
k=3: [order 48]
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EXAMPLE
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Some solutions for n=4 k=4
..3..3..1..3....1..1..3..1....3..3..3..1....3..3..1..3....3..3..1..3
..3..0..0..0....1..0..2..2....3..2..0..0....3..0..0..2....3..0..2..2
..1..0..2..0....3..0..0..2....3..0..2..2....1..0..0..0....1..0..2..2
..3..0..0..3....1..2..2..2....1..2..0..0....3..2..1..1....3..2..1..2
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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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