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....2....4....6...10...14...20...26...18....2
.3....2....4...10...22...38...60..110..138..188..106..108...54...36....4
.4....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354...292...16
.5....2....4...10...22...50..104..234..460..778..894.1540.1812.3444.3512.8294.6104.13914.5778.5548.2216..710...24
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 <= 7 are 11, 16, 20, 24, 29, 33. Reading this array by rows gives the sequence. The asymptotic sequence for the number of distinct shapes under rotation of the complete non-self-adjacent simple paths of each nodal length k for n >= k-1 is 2, 4, 10, 22, 50, 104 for which there appears to be no obvious formula.
LINKS
EXAMPLE
T(2,3) = The number of distinct shapes under rotation of the complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 7 node rectangle.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Christopher Hunt Gribble, Jun 12 2012
STATUS
approved