A213425 Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.

4, 4, 6, 10, 14, 20, 30, 40, 34, 10, 4, 8, 16, 22, 52, 68, 144, 222, 334, 406, 302, 288, 198, 88, 52, 6, 4, 8, 20, 40, 82, 124, 258, 400, 894, 1098, 1984, 1960, 2796, 2388, 3426, 2290, 2638, 1008, 1316, 152

Offset

2,1

Comments

The irregular array of numbers is:

...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20...21...22

.n

.2....4....4....6...10...14...20...30...40...34...10

.3....4....8...16...22...52...68..144..222..334..406..302..288..198...88...52....6

.4....4....8...20...40...82..124..258..400..894.1098.1984.1960.2796.2388.3426.2290.2638.1008.1316..152

where k is the path length in nodes. There is insufficient evidence to attempt to define the irregularity of the array. However, the maximum values of k for 2 <= n <= 10 are 12, 18, 22, 27, 32, 38, 42, 48, 52. Reading this array by rows gives the sequence. One half of the numbers of paths constitute the sequence to remove the effect of the bilateral symmetry of the rectangle.

Links

Table of n, a(n) for n=2..47.

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

T(2,3) = One half of the number of complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 8 node rectangle.

Crossrefs

Cf. A213106, A213249, A213274, A213089, A213342, A213375, A213379, A213383.

Sequence in context: A213379 A163976 A213383 * A213426 A054223 A160643

Adjacent sequences: A213422 A213423 A213424 * A213426 A213427 A213428

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jun 11 2012

Status

approved