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 A213473 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 4, n >= 2. 3
 2, 4, 6, 6, 2, 4, 10, 18, 8, 8, 14, 2, 4, 10, 18, 20, 12, 18, 8, 42, 2, 4, 10, 22, 46, 66, 60, 56, 106, 72, 236, 26, 2, 4, 10, 22, 50, 100, 152, 158, 230, 246, 410, 260, 546, 124, 32, 2, 4, 10, 22, 50, 104, 194, 300, 444, 542, 840, 650, 1056, 808, 1144, 354, 292, 16 (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 .n .2....2....4....6....6 .3....2....4...10...18....8....8...14 .4....2....4...10...18...20...12...18....8...42 .5....2....4...10...22...46...66...60...56..106...72..236...26 .6....2....4...10...22...50..100..152..158..230..246..410..260..546..124...32 .7....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354..292...16 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 <= 12 are 6, 9, 11, 14, 17, 20, 22, 25, 28, 30, 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, where n >= k-1, is 2, 4, 10, 22, 50, 104, 198, 354, 710, 1288, 2600 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 4 node rectangle. CROSSREFS Cf. A213106, A213249, A213431, A213433. Sequence in context: A141765 A234574 A010587 * A134920 A011031 A248844 Adjacent sequences:  A213470 A213471 A213472 * A213474 A213475 A213476 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jun 12 2012 STATUS approved

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Last modified August 2 20:05 EDT 2021. Contains 346428 sequences. (Running on oeis4.)