A214605 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.

186, 190, 192, 202, 1943, 2219, 2250, 2333, 2170, 2472, 2222, 2200, 18630, 23979, 26077, 26479, 24035, 23261, 20216, 20016, 184991, 259387, 298358, 300853, 269833, 254971, 232802, 232923, 307936, 238766, 178292, 178350

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 4 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......186....190....192....202

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

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

.5...184991.259387.298358.300853.269833.254971.232802.232923.307936.238766.178292.178350

where k indicates the position of a node in the quarter-rectangle.

For each n, the maximum value of k is 4*floor((n+1)/2).

Reading this array by rows gives the sequence.

Links

Table of n, a(n) for n=2..33.

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
NT 186 190 192 202 202 192 190 186
   186 190 192 202 202 192 190 186
To limit duplication, only the top left-hand corner 186 and the 190, 192, 202 to its right are stored in the sequence,
i.e. T(2,1) = 186, T(2,2) = 190, T(2,3) = 192 and T(2,4) = 202.

Crossrefs

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

Sequence in context: A203392 A197646 A015273 * A186398 A124207 A189941

Adjacent sequences: A214602 A214603 A214604 * A214606 A214607 A214608

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 22 2012

Status

approved