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 A214608 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths incorporating each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 9, n >= 2. 0
 304, 310, 314, 334, 334, 4137, 4754, 4811, 4929, 4920, 4610, 5260, 4738, 4784, 4924, 50775, 66474, 72137, 71469, 69764, 65977, 63790, 55400, 55907, 57274, 676474, 969677, 1118226, 1096104, 1058044, 1003962, 946620, 864012, 870946, 884912, 1154902, 887242, 651592, 669896, 710904 (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 5 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......13......14......15 .n .2......304.....310.....314.....334.....334 .3.....4137....4754....4811....4929....4920....4610....5260....4738....4784....4924 .4....50775...66474...72137...71469...69764...65977...63790...55400...55907...57274 .5...676474..969677.1118226.1096104.1058044.1003962..946620..864012..870946..884912.1154902..887242..651592..669896..710904 where k indicates the position of a node in the quarter-rectangle. For each n, the maximum value of k is 5*floor((n+1)/2). Reading this array by rows gives the sequence. LINKS Table of n, a(n) for n=2..41. C. H. Gribble, Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle. C. H. Gribble, Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively. EXAMPLE When n = 2, the number of times (NT) each node in the rectangle (N) occurs in a complete non-self-adjacent simple path is N 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 NT 304 310 314 334 334 334 314 310 304 304 310 314 334 334 334 314 310 304 To limit duplication, only the top left-hand corner 304 and the 310, 314, 334, 334 to its right are stored in the sequence, i.e. T(2,1) = 304, T(2,2) = 310, T(2,3) = 314, T(2,4) = 334 and T(2,5) = 334. CROSSREFS Cf. A213106, A213249, A213426, A214042, A214376, A214397, A214399, A214504, A214510, A214563, A214601, A214503, A214605 Sequence in context: A291132 A328277 A253394 * A158932 A270303 A187934 Adjacent sequences: A214605 A214606 A214607 * A214609 A214610 A214611 KEYWORD nonn,tabf AUTHOR Christopher Hunt Gribble, Jul 22 2012 STATUS approved

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Last modified December 5 05:37 EST 2023. Contains 367575 sequences. (Running on oeis4.)