%I #6 Jul 23 2012 12:48:57

%S 186,190,192,202,1943,2219,2250,2333,2170,2472,2222,2200,18630,23979,

%T 26077,26479,24035,23261,20216,20016,184991,259387,298358,300853,

%U 269833,254971,232802,232923,307936,238766,178292,178350

%N 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 8, 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......186....190....192....202

%C .3.....1943...2219...2250...2333...2170...2472...2222...2200

%C .4....18630..23979..26077..26479..24035..23261..20216..20016

%C .5...184991.259387.298358.300853.269833.254971.232802.232923.307936.238766.178292.178350

%C where k indicates the position of a 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 (N) occurs in a complete non-self-adjacent simple path is

%e N 0 1 2 3 4 5 6 7

%e 8 9 10 11 12 13 14 15

%e NT 186 190 192 202 202 192 190 186

%e 186 190 192 202 202 192 190 186

%e To limit duplication, only the top left-hand corner 186 and the 190, 192, 202 to its right are stored in the sequence,

%e i.e. T(2,1) = 186, T(2,2) = 190, T(2,3) = 192 and T(2,4) = 202.

%Y Cf. A213106, A213249, A213425, A214038, A214375, A214397, A214399, A214504, A214510, A214563, A214601, A214503

%K nonn,tabf

%O 2,1

%A _Christopher Hunt Gribble_, Jul 22 2012