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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 7, n >= 2.
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%I #10 Jul 23 2012 12:46:23

%S 52,0,0,0,353,57,62,60,10,0,0,0,1931,495,622,602,200,56,262,364,12027,

%T 3522,4399,4170,2143,640,1941,2394,2612,954,3956,5136,76933,21068,

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

%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 7, 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 4 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......52.....0.....0.....0

%C .3.....353....57....62....60....10.....0.....0.....0

%C .4....1931...495...622...602...200....56...262...364

%C .5...12027..3522..4399..4170..2143...640..1941..2394..2612...954..3956..5136

%C .6...76933.21068.26181.25090.17601..3675..9258.10048.20009..7213.26414.32132

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

%C For each n, the maximum value of k is 4*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 6

%e 7 8 9 10 11 12 13

%e NT 52 0 0 0 0 0 52

%e 52 0 0 0 0 0 52

%e To limit duplication, only the top left-hand corner 52 and the three zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0, T(2,3) = 0 and T(2,4) = 0.

%Y Cf. A213106, A213249, A213383, A214037, A214119, A214121, A214122, A214359, A213070.

%K nonn,tabf

%O 2,1

%A _Christopher Hunt Gribble_, Jul 14 2012

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