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 A213431 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 2, n >= 2. 5
 2, 2, 4, 2, 2, 4, 6, 6, 2, 4, 6, 10, 10, 2, 2, 4, 6, 10, 14, 16, 8, 2, 4, 6, 10, 14, 20, 26, 18, 2, 2, 4, 6, 10, 14, 20, 30, 40, 34, 10, 2, 4, 6, 10, 14, 20, 30, 44, 60, 60, 28, 2, 2, 4, 6, 10, 14, 20, 30, 44, 64, 90, 100, 62, 12 (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 ..n ..2....2 ..3....2...4...2 ..4....2...4...6...6 ..5....2...4...6..10..10...2 ..6....2...4...6..10..14..16...8 ..7....2...4...6..10..14..20..26..18...2 ..8....2...4...6..10..14..20..30..40..34..10 ..9....2...4...6..10..14..20..30..44..60..60..28...2 .10....2...4...6..10..14..20..30..44..64..90.100..62..12 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 n + floor((n+1)/2) for n >= 2. Reading this array by rows gives the sequence. LINKS FORMULA 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 >> 0 appears to be 2*A097333(2:), that is, 2*(Sum(j=0..k-2, C(k-2-j, floor(j/2)))), for k >= 4. 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 2 node rectangle. CROSSREFS Cf. A213106, A213249. Sequence in context: A118232 A115070 A064145 * A331985 A261891 A321320 Adjacent sequences:  A213428 A213429 A213430 * A213432 A213433 A213434 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jun 11 2012 STATUS approved

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Last modified April 10 20:17 EDT 2021. Contains 342856 sequences. (Running on oeis4.)