A214510 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 4, n >= 2.

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

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 2 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

.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 quarter-rectangle.

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 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
NT 23 24 24 23
   23 24 24 23
To limit duplication, only the top left-hand 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