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 A213474 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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. LINKS EXAMPLE 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. CROSSREFS Cf. A213106, A213249, A213431, A213433, A213473. Sequence in context: A243501 A076246 A100426 * A187333 A321805 A333412 Adjacent sequences:  A213471 A213472 A213473 * A213475 A213476 A213477 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jun 12 2012 STATUS approved

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Last modified May 18 03:30 EDT 2022. Contains 353783 sequences. (Running on oeis4.)