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 A213274 Irregular array T(n,k) of numbers/2 of 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. 10
 4, 4, 4, 2, 4, 4, 6, 6, 4, 4, 6, 10, 10, 2, 4, 4, 6, 10, 14, 16, 8, 4, 4, 6, 10, 14, 20, 26, 18, 2, 4, 4, 6, 10, 14, 20, 30, 40, 34, 10, 4, 4, 6, 10, 14, 20, 30, 44, 60, 60, 28, 2, 4, 4, 6, 10, 14, 20, 30, 44, 64, 90, 100, 62, 12, 4, 4, 6, 10, 14, 20, 30, 44, 64, 94, 134, 160, 122, 40, 2 (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 ..n ..2....4 ..3....4...4...2 ..4....4...4...6...6 ..5....4...4...6..10..10...2 ..6....4...4...6..10..14..16...8 ..7....4...4...6..10..14..20..26..18...2 ..8....4...4...6..10..14..20..30..40..34..10 ..9....4...4...6..10..14..20..30..44..60..60..28...2 .10....4...4...6..10..14..20..30..44..64..90.100..62..12 .11....4...4...6..10..14..20..30..44..64..94.134.160.122..40...2 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 + n mod 2)/2 for n >= 2. 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 a rectangle. LINKS FORMULA The asymptotic sequence for the number of paths of each nodal length k for n >> 0 appears to be 2*A097333(1:), that is, 2*(Sum(j=0..k-2, C(k-2-j, floor(j/2)))), for k >= 3. 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 2 node rectangle. CROSSREFS Cf. A213106, A213249. Sequence in context: A220668 A109610 A067395 * A182565 A016708 A105724 Adjacent sequences:  A213271 A213272 A213273 * A213275 A213276 A213277 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jun 08 2012 STATUS approved

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Last modified November 30 18:46 EST 2021. Contains 349424 sequences. (Running on oeis4.)