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A213375
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Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.
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8
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4, 4, 6, 10, 10, 2, 4, 8, 16, 22, 42, 24, 42, 22, 18, 4, 8, 20, 40, 72, 80, 90, 66, 184, 72, 236, 26, 4, 8, 20, 44, 100, 136, 220, 156, 348, 244, 800, 336, 1308, 248, 56, 4, 8, 20, 44, 106, 172, 322, 410, 612, 602, 1462, 1122, 3240, 1712, 4682, 1394, 706, 218, 4
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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....4....4....6...10...10....2
.3....4....8...16...22...42...24...42...22...18
.4....4....8...20...40...72...80...90...66..184...72..236...26
.5....4....8...20...44..100..136..220..156..348..244..800..336.1308..248....56
.6....4....8...20...44..106..172..322..410..612..602.1462.1122.3240.1712..4682.1394...706..218...4
where k is the path length in nodes. In an attempt to define the irregularity of the array, it appears that the maximum value of k is 3n+2 for 2 <= n <= 5, 3n+3 for 6 <= n <= 9 and 3n+4 for n >= 10. Reading this array by rows gives the sequence. One half of the numbers of paths constitute the sequence to remove the effect of the bilateral symmetry of the rectangle.
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LINKS
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EXAMPLE
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T(2,3) = One half of the number of complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 5 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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