

A213375


Irregular array T(n,k) of numbers/2 of nonextendable (complete) nonselfadjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.


8



4, 4, 6, 10, 10, 2, 4, 8, 16, 22, 42, 24, 42, 22, 18, 4, 8, 20, 40, 72, 80, 90, 66, 184, 72, 236, 26, 4, 8, 20, 44, 100, 136, 220, 156, 348, 244, 800, 336, 1308, 248, 56, 4, 8, 20, 44, 106, 172, 322, 410, 612, 602, 1462, 1122, 3240, 1712, 4682, 1394, 706, 218, 4
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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...23...24
.n
.2....4....4....6...10...10....2
.3....4....8...16...22...42...24...42...22...18
.4....4....8...20...40...72...80...90...66..184...72..236...26
.5....4....8...20...44..100..136..220..156..348..244..800..336.1308..248....56
.6....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 3n+2 for 2 <= n <= 5, 3n+3 for 6 <= n <= 9 and 3n+4 for n >= 10. 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..62.
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

T(2,3) = One half of the number of complete nonselfadjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 5 node rectangle.


CROSSREFS

Cf. A213106, A213249, A213274, A213089, A213342.
Sequence in context: A128037 A102414 A127799 * A226834 A098052 A098530
Adjacent sequences: A213372 A213373 A213374 * A213376 A213377 A213378


KEYWORD

nonn,tabf


AUTHOR

Christopher Hunt Gribble, Jun 10 2012


STATUS

approved



