

A214510


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 4, n >= 2.


5



23, 24, 80, 86, 88, 100, 264, 303, 303, 282, 820, 1008, 1007, 907, 1058, 776, 2401, 3043, 3013, 2844, 3312, 2375, 6751, 8651, 8562, 8317, 9411, 7116, 9718, 6882, 18630, 24035, 23979, 23261, 26077, 20216, 26479, 20016, 50775, 65977, 66474, 63790, 72137, 55400, 71469, 55907, 69764, 57274
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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 2 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
.n
.2......23....24
.3......80....86....88...100
.4.....264...303...303...282
.5.....820..1008..1007...907..1058...776
.6....2401..3043..3013..2844..3312..2375
.7....6751..8651..8562..8317..9411..7116..9718..6882
.8...18630.24035.23979.23261.26077.20216.26479.20016
.9...50775.65977.66474.63790.72137.55400.71469.55907.69764.57274
where k indicates the position of a node in the quarterrectangle.
For each n, the maximum value of k is 2*floor((n+1)/2).
Reading this array by rows gives the sequence.


LINKS

Table of n, a(n) for n=2..49.
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
NT 23 24 24 23
23 24 24 23
To limit duplication, only the top lefthand corner 23 and the 24 to its right are stored in the sequence,
i.e. T(2,1) = 23 and T(2,2) = 24.


CROSSREFS

Cf. A213106, A213249, A213342, A214022, A214122, A214397, A214399, A214504
Sequence in context: A042080 A042076 A042074 * A042084 A042082 A042088
Adjacent sequences: A214507 A214508 A214509 * A214511 A214512 A214513


KEYWORD

nonn,tabf


AUTHOR

Christopher Hunt Gribble, Jul 19 2012


EXTENSIONS

Comment corrected by Christopher Hunt Gribble, Jul 22 2012


STATUS

approved



