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A213473
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Irregular array T(n,k) of the numbers of distinct shapes under rotation of the non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2.
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3
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2, 4, 6, 6, 2, 4, 10, 18, 8, 8, 14, 2, 4, 10, 18, 20, 12, 18, 8, 42, 2, 4, 10, 22, 46, 66, 60, 56, 106, 72, 236, 26, 2, 4, 10, 22, 50, 100, 152, 158, 230, 246, 410, 260, 546, 124, 32, 2, 4, 10, 22, 50, 104, 194, 300, 444, 542, 840, 650, 1056, 808, 1144, 354, 292, 16
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OFFSET
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2,1
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COMMENTS
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The irregular array of numbers is:
...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20
.n
.2....2....4....6....6
.3....2....4...10...18....8....8...14
.4....2....4...10...18...20...12...18....8...42
.5....2....4...10...22...46...66...60...56..106...72..236...26
.6....2....4...10...22...50..100..152..158..230..246..410..260..546..124...32
.7....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354..292...16
where k is the path length in nodes. There is insufficient evidence to attempt to define the irregularity of the array. However, the maximum values of k for 2 <= n <= 12 are 6, 9, 11, 14, 17, 20, 22, 25, 28, 30, 33. Reading this array by rows gives the sequence. The asymptotic sequence for the number of distinct shapes under rotation of the complete non-self-adjacent simple paths of each nodal length k, where n >= k-1, is 2, 4, 10, 22, 50, 104, 198, 354, 710, 1288, 2600 for which there appears to be no obvious formula.
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LINKS
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EXAMPLE
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T(2,3) = The number of distinct shapes under rotation of the complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 4 node rectangle.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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