

A214605


Irregular array T(n,k) of the numbers of nonextendable (complete) nonselfadjacent 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.


1



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
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OFFSET

2,1


COMMENTS

The subset of nodes is contained in the top lefthand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 4 to capture all geometrically distinct counts.
The quarterrectangle 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 quarterrectangle.
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 nonselfadjacent paths in a square lattice bounded by various sizes of rectangle.
C. H. Gribble, Computes characteristics of complete nonselfadjacent 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 nonselfadjacent 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 lefthand 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



