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A213476
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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 7, n >= 2.
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0
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2, 4, 6, 10, 14, 20, 26, 18, 2, 2, 4, 10, 22, 38, 60, 110, 138, 188, 106, 108, 54, 36, 4, 2, 4, 10, 22, 50, 104, 194, 300, 444, 542, 840, 650, 1056, 808, 1144, 354, 292, 16, 2, 4, 10, 22, 50, 104, 234, 460, 778, 894, 1540, 1812, 3444, 3512, 8294, 6104, 13914, 5778, 5548, 2216, 710, 24
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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...21...22...23...24
.n
.2....2....4....6...10...14...20...26...18....2
.3....2....4...10...22...38...60..110..138..188..106..108...54...36....4
.4....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354...292...16
.5....2....4...10...22...50..104..234..460..778..894.1540.1812.3444.3512.8294.6104.13914.5778.5548.2216..710...24
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 <= 7 are 11, 16, 20, 24, 29, 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 for n >= k-1 is 2, 4, 10, 22, 50, 104 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 7 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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