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A204754
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T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order
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9
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40, 61, 61, 102, 46, 102, 188, 31, 31, 188, 342, 28, 22, 28, 342, 590, 38, 27, 27, 38, 590, 1051, 49, 35, 32, 35, 49, 1051, 1915, 70, 48, 40, 40, 48, 70, 1915, 3308, 106, 69, 53, 48, 53, 69, 106, 3308, 5967, 159, 103, 74, 61, 61, 74, 103, 159, 5967, 10934, 248, 158, 108
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OFFSET
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1,1
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COMMENTS
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Table starts
...40..61.102.188.342.590.1051.1915.3308.5967.10934.19151.34428.62824.110673
...61..46..31..28..38..49...70..106..159..248...394...625..1002..1614...2599
..102..31..22..27..35..48...69..103..158..247...391...624..1001..1611...2598
..188..28..27..32..40..53...74..108..163..252...396...629..1006..1616...2603
..342..38..35..40..48..61...82..116..171..260...404...637..1014..1624...2611
..590..49..48..53..61..74...95..129..184..273...417...650..1027..1637...2624
.1051..70..69..74..82..95..116..150..205..294...438...671..1048..1658...2645
.1915.106.103.108.116.129..150..184..239..328...472...705..1082..1692...2679
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LINKS
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FORMULA
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Empirical for columns:
k>2: a(n) = 2*a(n-1) -a(n-3) for n>5
k=2: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8
k=1: a(n) = 3*a(n-1) -2*a(n-2) +3*a(n-3) -10*a(n-4) +7*a(n-5) +7*a(n-6) -17*a(n-7) +6*a(n-8) +6*a(n-9) +4*a(n-10) -2*a(n-11) +4*a(n-12) -16*a(n-13) +8*a(n-14) for n>15
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EXAMPLE
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Some solutions for n=3 k=3
..0..0..0..1..1....0..1..0..1..1....0..1..0..0..1....0..0..0..0..0
..0..0..1..1..1....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
..0..1..1..1..0....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
..1..1..1..0..0....0..1..0..1..1....0..1..0..0..1....0..0..0..0..0
..1..1..0..0..0....0..1..0..1..1....0..1..0..0..1....1..1..1..1..1
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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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