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A213475
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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 6, n >= 2.
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1
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2, 4, 6, 10, 14, 16, 8, 2, 4, 10, 22, 38, 56, 68, 80, 58, 34, 24, 2, 2, 4, 10, 22, 50, 100, 152, 158, 230, 246, 410, 260, 546, 124, 32, 2, 4, 10, 22, 50, 100, 192, 318, 340, 430, 726, 816, 1786, 1454, 4626, 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
.n
.2....2....4....6...10...14...16....8
.3....2....4...10...22...38...56...68...80...58...34...24....2
.4....2....4...10...22...50..100..152..158..230..246..410..260..546..124...32
.5....2....4...10...22...50..100..192..318..340..430..726..816.1786.1454.4626.1394..706..218....4
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 9, 14, 17, 21, 24, 29. 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 6 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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