login
A213342
Irregular array T(n,k) of numbers/2 of non-extendable non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2.
8
4, 4, 6, 6, 4, 8, 16, 18, 14, 8, 14, 4, 8, 20, 36, 44, 24, 40, 16, 84, 4, 8, 20, 40, 72, 80, 90, 66, 184, 72, 236, 26, 4, 8, 20, 40, 78, 116, 192, 180, 354, 278, 530, 268, 546, 124, 32, 4, 8, 20, 40, 80, 122, 244, 336, 628, 628, 1130, 788, 1362, 878, 1168, 354, 292, 16
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
.n
.2....4....4....6....6
.3....4....8...16...18...14....8...14
.4....4....8...20...36...44...24...40...16...84
.5....4....8...20...40...72...80...90...66..184...72..236...26
.6....4....8...20...40...78..116..192..180..354..278..530..268..546..124...32
.7....4....8...20...40...80..122..244..336..628..628.1130..788.1362..878.1168..354..292...16
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 for 2 <= n <= 3, 3n-1 for n = 4 and 3n - floor((n-2)/3) for n >= 5. 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.
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 4 node rectangle.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved