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A240338
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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 one plus the sum of the elements diagonally to its northwest, modulo 4
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6
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2, 4, 4, 7, 15, 7, 11, 48, 48, 11, 16, 125, 316, 125, 16, 22, 284, 1543, 1543, 284, 22, 29, 582, 6271, 14456, 6271, 582, 29, 37, 1097, 22116, 110327, 110327, 22116, 1097, 37, 46, 1932, 69596, 716770, 1607848, 716770, 69596, 1932, 46, 56, 3219, 199504, 4106515
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OFFSET
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1,1
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COMMENTS
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Table starts
..2....4.......7........11...........16............22.............29
..4...15......48.......125..........284...........582...........1097
..7...48.....316......1543.........6271.........22116..........69596
.11..125....1543.....14456.......110327........716770........4106515
.16..284....6271....110327......1607848......19629542......208224462
.22..582...22116....716770.....19629542.....455506837.....9073358239
.29.1097...69596...4106515....208224462....9073358239...342013040533
.37.1932..199504..21225132...1979743527..160455447637.11361329151015
.46.3219..528924.100450928..17168302936.2579449716281
.56.5123.1310622.439636230.137234695613
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
k=2: [polynomial of degree 5] for n>2
k=3: [polynomial of degree 13] for n>12
k=4: [polynomial of degree 30] for n>35
k=5: [polynomial of degree 69] for n>88
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..3..3....0..0..0..0....0..0..0..0....3..0..0..3....0..3..3..3
..0..0..3..3....0..3..0..3....0..0..3..3....0..3..3..2....0..0..3..2
..3..3..2..1....0..0..3..2....0..3..2..2....3..0..2..2....3..3..3..0
..3..2..1..2....0..0..0..0....0..3..2..0....3..3..2..0....3..2..2..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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