A213379 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 6, n >= 2.

4, 4, 6, 10, 14, 16, 8, 4, 8, 16, 22, 48, 60, 82, 90, 66, 34, 24, 2, 4, 8, 20, 40, 78, 116, 192, 180, 354, 278, 530, 268, 546, 124, 32, 4, 8, 20, 44, 106, 172, 322, 410, 612, 602, 1462, 1122, 3240, 1712, 4682, 1394, 706, 218, 4

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

.n

.2....4....4....6...10...14...16....8

.3....4....8...16...22...48...60...82...90...66...34...24....2

.4....4....8...20...40...78..116..192..180..354..278..530..268..546..124...32

.5....4....8...20...44..106..172..322..410..612..602.1462.1122.3240.1712.4682.1394..706..218....4

where k is the path length in nodes. In an attempt to define the irregularity of the array, it appears that the maximum value of k is 4n - floor((n-8)/4) for n >= 8. 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..54.

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 6 node rectangle.

Crossrefs

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

Sequence in context: A226834 A098052 A098530 * A163976 A213383 A213425

Adjacent sequences: A213376 A213377 A213378 * A213380 A213381 A213382

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jun 10 2012

Status

approved