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 A213478 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 2, n >= 2. 9
 2, 3, 4, 5, 5, 8, 7, 6, 13, 10, 8, 21, 15, 11, 10, 34, 23, 16, 13, 55, 36, 24, 18, 16, 89, 57, 37, 26, 21, 144, 91, 58, 39, 29, 26, 233, 146, 92, 60, 42, 34, 377, 235, 147, 94, 63, 47, 42, 610, 379, 236, 149, 97, 68, 55, 987, 612, 380, 238, 152, 102, 76, 68, 1597, 989, 613, 382, 241, 157, 110, 89 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The subset of nodes approximately defines the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 1 to capture all geometrically distinct counts. The quarter-rectangle is read by rows. The irregular array of numbers is: ....k.....1...2...3...4...5...6...7...8 ..n ..2.......2 ..3.......3...4 ..4.......5...5 ..5.......8...7...6 ..6......13..10...8 ..7......21..15..11..10 ..8......34..23..16..13 ..9......55..36..24..18..16 .10......89..57..37..26..21 .11.....144..91..58..39..29..26 .12.....233.146..92..60..42..34 .13.....377.235.147..94..63..47..42 .14.....610.379.236.149..97..68..55 .15.....987.612.380.238.152.102..76..68 .16....1597.989.613.382.241.157.110..89 where k indicates the position of the start node in the quarter-rectangle. For each n, the maximum value of k is floor((n+1)/2). Reading this array by rows gives the sequence. LINKS FORMULA Let T(n,k) denote an element of the irregular array then it appears that T(n,k) = A000045(n-k+2), k = 0 T(n,k) = A000045(n-k+2) + A000045(k+1), k > 0. EXAMPLE When n = 2, the number of times (NT) each node in the rectangle is the start node (SN) of a complete non-self-adjacent simple path is SN 0 1    2 3 NT 2 2    2 2 To limit duplication, only the top left-hand corner 2 is stored in the sequence, i.e. T(2,1) = 2. CROSSREFS Cf. A213106, A213249, A213274. Sequence in context: A017844 A303655 A011156 * A266449 A265536 A037849 Adjacent sequences:  A213475 A213476 A213477 * A213479 A213480 A213481 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jun 12 2012 EXTENSIONS Improved Comments STATUS approved

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Last modified July 17 16:38 EDT 2019. Contains 325107 sequences. (Running on oeis4.)