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A204370
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T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..2 introduced in row major order
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9
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74, 212, 212, 555, 466, 555, 891, 673, 673, 891, 2419, 713, 342, 713, 2419, 6121, 1715, 622, 622, 1715, 6121, 13693, 4355, 1042, 704, 1042, 4355, 13693, 38041, 11671, 2574, 1264, 1264, 2574, 11671, 38041, 99753, 31891, 6786, 2956, 1984, 2956, 6786, 31891
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OFFSET
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1,1
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COMMENTS
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Table starts
....74...212...555...891..2419..6121.13693.38041.99753.256077.702265.1904821
...212...466...673...713..1715..4355.11671.31891.86275.235547.643475.1756499
...555...673...342...622..1042..2574..6786.17586.47674.130066.353650..965730
...891...713...622...704..1264..2956..6772.17852.48260.129860.354004..966724
..2419..1715..1042..1264..1984..3280..7376.18776.48392.130552.355336..966472
..6121..4355..2574..2956..3280..4856..9272.19880.50056.132856.356056..968312
.13693.11671..6786..6772..7376..9272.12896.24064.54880.136096.360416..973952
.38041.31891.17586.17852.18776.19880.24064.35872.65104.147440.373040..983408
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 5*a(n-1) -7*a(n-2) +3*a(n-3) -6*a(n-4) +12*a(n-5) +14*a(n-6) -84*a(n-7) +164*a(n-8) -292*a(n-9) +392*a(n-10) -392*a(n-11) +640*a(n-12) -896*a(n-13) +64*a(n-14) +2176*a(n-15) -3584*a(n-16) +2304*a(n-17) -512*a(n-18)
k=2..7: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>9
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EXAMPLE
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Some solutions for n=5 k=3
..0..0..0..1..0....0..0..0..0..0....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....1..1..1..1..1....0..1..0..0..1....1..1..1..1..0
..1..1..1..1..1....2..2..2..2..2....0..1..0..0..1....0..0..0..0..0
..0..0..0..0..0....1..1..1..1..1....0..1..0..0..1....0..0..0..0..0
..1..1..1..1..1....2..2..2..2..2....0..1..0..0..1....1..1..1..1..1
..1..1..1..1..1....2..2..2..2..2....0..0..0..0..1....1..1..1..1..1
..0..1..0..0..0....1..2..0..0..0....1..1..0..0..1....2..1..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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