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 A214121 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 3, n >= 2. 7
 5, 0, 14, 2, 2, 0, 33, 4, 6, 0, 75, 6, 13, 0, 16, 0, 165, 8, 27, 0, 32, 0, 353, 10, 57, 0, 62, 0, 60, 0, 747, 12, 119, 0, 124, 0, 109, 0, 1577, 14, 247, 0, 250, 0, 206, 0, 184, 0, 3327, 16, 515, 0, 508, 0, 399, 0, 323, 0, 7015, 18, 1079, 0, 1046, 0, 790, 0, 590 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 2 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.....9....10....11....12 ..n ..2.......5.....0 ..3......14.....2.....2.....0 ..4......33.....4.....6.....0 ..5......75.....6....13.....0....16.....0 ..6.....165.....8....27.....0....32.....0 ..7.....353....10....57.....0....62.....0....60.....0 ..8.....747....12...119.....0...124.....0...109.....0 ..9....1577....14...247.....0...250.....0...206.....0...184.....0 .10....3327....16...515.....0...508.....0...399.....0...323.....0 .11....7015....18..1079.....0..1046.....0...790.....0...590.....0...520.....0 .12...14785....20..2267.....0..2176.....0..1601.....0..1121.....0...877.....0 where k indicates the position of the end node in the quarter-rectangle. For each n, the maximum value of k is 2*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) = 0, n >= 3, k = 2j, j >= 2, T(n,1) - 2T(n-1,1) - T(n-4,1) - 8 = 0, n >= 8, T(n,2) = 2(n-2), n >= 2, T(n,3) - 2T(n-1,3) - T(n-4,3) + 2(n-7) = 0, n >= 9, T(n,5) - 2T(n-1,5) - T(n-4,5) + 8(n-7) = 0, n >= 10, T(n,7) - 2T(n-1,7) - T(n-4,7) + 20(n-8) + 8 = 0, n >= 11, T(n,9) - 2T(n-1,9) - T(n-4,9) + 46(n-9) + 30 = 0, n >= 13, T(n,11) - 2T(n-1,11) - T(n-4,11) + 104(n-10) + 84 = 0, n >= 15, T(n,13) - 2T(n-1,13) - T(n-4,13) + 226(n-11) + 202 = 0, n >= 15. EXAMPLE When n = 2, the number of times (NT) each node in the rectangle is the end node (EN) of a complete non-self-adjacent simple path is EN 0 1 2    3 4 5 NT 5 0 5    5 0 5 To limit duplication, only the top left-hand corner 5 and the 0 to its right are stored in the sequence, i.e. T(2,1) = 5 and T(2,2) = 0. CROSSREFS Cf. A213106, A213249, A213089, A213954, A214119. Sequence in context: A292105 A052401 A222946 * A024418 A167297 A290867 Adjacent sequences:  A214118 A214119 A214120 * A214122 A214123 A214124 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jul 04 2012 EXTENSIONS Comment corrected by Christopher Hunt Gribble, Jul 22 2012 STATUS approved

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Last modified June 15 22:19 EDT 2019. Contains 324145 sequences. (Running on oeis4.)