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A213474
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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 5, n >= 2.
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2
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2, 4, 6, 10, 10, 2, 2, 4, 10, 22, 34, 22, 36, 22, 18, 2, 4, 10, 22, 46, 66, 60, 56, 106, 72, 236, 26, 2, 4, 10, 22, 46, 66, 100, 76, 132, 116, 314, 160, 654, 124, 28, 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...10....2
.3....2....4...10...22...34...22...36...22...18
.4....2....4...10...22...46...66...60...56..106...72..236...26
.5....2....4...10...22...46...66..100...76..132..116..314..160..654..124...28
.6....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 <= 9 are 8, 11, 14, 17, 21, 24, 27, 30. 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, 238, 514 for which there appears to be no obvious formula.
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LINKS
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Table of n, a(n) for n=2..62.
C. H. Gribble, Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.
C. H. Gribble, Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.
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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 5 node rectangle.
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CROSSREFS
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Cf. A213106, A213249, A213431, A213433, A213473.
Sequence in context: A243501 A076246 A100426 * A187333 A321805 A333412
Adjacent sequences: A213471 A213472 A213473 * A213475 A213476 A213477
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KEYWORD
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nonn,tabf
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AUTHOR
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Christopher Hunt Gribble, Jun 12 2012
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STATUS
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approved
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