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 A213342 Irregular array T(n,k) of numbers/2 of non-extendable non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2. 8
 4, 4, 6, 6, 4, 8, 16, 18, 14, 8, 14, 4, 8, 20, 36, 44, 24, 40, 16, 84, 4, 8, 20, 40, 72, 80, 90, 66, 184, 72, 236, 26, 4, 8, 20, 40, 78, 116, 192, 180, 354, 278, 530, 268, 546, 124, 32, 4, 8, 20, 40, 80, 122, 244, 336, 628, 628, 1130, 788, 1362, 878, 1168, 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....4....4....6....6 .3....4....8...16...18...14....8...14 .4....4....8...20...36...44...24...40...16...84 .5....4....8...20...40...72...80...90...66..184...72..236...26 .6....4....8...20...40...78..116..192..180..354..278..530..268..546..124...32 .7....4....8...20...40...80..122..244..336..628..628.1130..788.1362..878.1168..354..292...16 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 for 2 <= n <= 3, 3n-1 for n = 4 and 3n - floor((n-2)/3) for n >= 5. 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. LINKS EXAMPLE 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 4 node rectangle. CROSSREFS Cf. A213106, A213249, A213274, A213089. Sequence in context: A016710 A225134 A121064 * A019559 A274636 A198697 Adjacent sequences:  A213339 A213340 A213341 * A213343 A213344 A213345 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jun 09 2012 STATUS approved

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Last modified May 26 22:58 EDT 2020. Contains 334634 sequences. (Running on oeis4.)