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A209534
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T(n,k)=Half the number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences
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6
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5, 9, 9, 17, 25, 17, 33, 65, 65, 33, 65, 193, 257, 193, 65, 129, 513, 1025, 1025, 513, 129, 257, 1537, 4097, 6145, 4097, 1537, 257, 513, 4097, 16385, 32769, 32769, 16385, 4097, 513, 1025, 12289, 65537, 196609, 262145, 196609, 65537, 12289, 1025, 2049, 32769
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OFFSET
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1,1
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COMMENTS
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Table starts
...5.....9.....17......33........65........129.........257...........513
...9....25.....65.....193.......513.......1537........4097.........12289
..17....65....257....1025......4097......16385.......65537........262145
..33...193...1025....6145.....32769.....196609.....1048577.......6291457
..65...513...4097...32769....262145....2097153....16777217.....134217729
.129..1537..16385..196609...2097153...25165825...268435457....3221225473
.257..4097..65537.1048577..16777217..268435457..4294967297...68719476737
.513.12289.262145.6291457.134217729.3221225473.68719476737.1649267441665
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LINKS
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FORMULA
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Empirical: for odd columns k T(n,k) = 2^((n+1)*(k+1)/2)+1
Empirical for even columns k:
k=2: a(n) = a(n-1) +8*a(n-2) -8*a(n-3)
k=4: a(n) = a(n-1) +32*a(n-2) -32*a(n-3)
k=6: a(n) = a(n-1) +128*a(n-2) -128*a(n-3)
Apparently for even k a(n) = a(n-1) +2^(k+1)*a(n-2) -2^(k+1)*a(n-3)
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EXAMPLE
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Some solutions for n=4 k=3
..1..2..1..2....0..1..2..1....2..0..2..0....1..2..1..2....0..1..0..1
..2..1..0..1....1..0..1..0....0..2..0..2....2..1..2..1....1..2..1..2
..1..2..1..0....2..1..0..1....2..0..2..0....1..2..1..2....2..1..0..1
..2..1..2..1....1..0..1..0....0..2..0..2....2..1..2..1....1..2..1..2
..1..2..1..2....2..1..0..1....2..0..2..0....1..2..1..0....2..1..0..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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