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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 6, n >= 2.
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%I #25 Jul 23 2012 12:46:36

%S 31,0,0,165,27,32,8,0,0,720,187,236,104,30,108,3431,992,1179,746,251,

%T 580,920,352,1210,16608,4361,5027,4361,1094,2043,5027,2043,6268,76933,

%U 17601,20009,21068,3675,7213,26181,9258,26414,25090,10048,32132

%N 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 6, n >= 2.

%C The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 3 to capture all geometrically distinct counts.

%C The quarter-rectangle is read by rows.

%C The irregular array of numbers is:

%C ...k.....1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12

%C .n

%C .2......31.....0.....0

%C .3.....165....27....32.....8.....0.....0

%C .4.....720...187...236...104....30...108

%C .5....3431...992..1179...746...251...580...920...352..1210

%C .6...16608..4361..5027..4361..1094..2043..5027..2043..6268

%C .7...76933.17601.20009.21068..3675..7213.26181..9258.26414.25090.10048.32132

%C where k indicates the position of the end node in the quarter-rectangle.

%C For each n, the maximum value of k is 3*floor((n+1)/2).

%C Reading this array by rows gives the sequence.

%H C. H. Gribble, <a href="https://oeis.org/wiki/Complete_non-self-adjacent_paths:Results_for_Square_Lattice">Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.</a>

%H C. H. Gribble, <a href="https://oeis.org/wiki/Complete non-self-adjacent paths:Program">Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.</a>

%e 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

%e EN 0 1 2 3 4 5

%e 6 7 8 9 10 11

%e NT 31 0 0 0 0 31

%e 31 0 0 0 0 31

%e To limit duplication, only the top left-hand corner 31 and the two zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0 and T(2,3) = 0.

%Y Cf. A213106, A213249, A213379, A214025, A214119, A214121, A214122, A214359.

%K nonn,tabf

%O 2,1

%A _Christopher Hunt Gribble_, Jul 13 2012

%E Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012