[seqfan] Periodic Square-Free Series

[Ron Hardin]

Analogous to square free series http://oeis.org/A006156 consider periodic 
square-free series

T(n,k)=Number of length n 0..k arrays connected end-around, with no sequence of 
l<n elements immediately followed by itself (periodic "square-free")

Table starts
.2..3......4........5.........6.........7.........8.........9........10
.2..6.....12.......20........30........42........56........72........90
.0..6.....24.......60.......120.......210.......336.......504.......720
.0.12.....72......240.......600......1260......2352......4032......6480
.0..0....120......720......2520......6720.....15120.....30240.....55440
.0.18....408.....2940.....12600.....40110....105168....240408....496080
.0..0....840....10080.....57960....228480....710640...1874880...4379760
.0.24...2448....38640....280560...1338120...4883424..14783328..38962080
.0..0...5760...140400...1330560...7761600..33384960.116212320.345945600
.0..0..15960...529440...6394680..45291120.228945360....................
.0.66..39864..1956900..30548760.263674950..............................
.0.72.108024..7335840.146516040........................................
.0.78.275184.27285180..................................................
.0..0.728784...........................................................
.0.30..................................................................

and restricting the order of first appearance of 0..k to strictly increasing

T(n,k)=Number of length n 0..k arrays connected end-around, with no sequence of 
l<n elements immediately followed by itself (periodic "square-free"), and new 
values introduced in order 0..k

Table starts
.1..1....1.....1....1....1...1..1..1.1.1.1.1.1
.1..1....1.....1....1....1...1..1..1.1.1.1.1..
.0..1....1.....1....1....1...1..1..1.1.1.1....
.0..2....3.....3....3....3...3..3..3.3.3......
.0..0....5.....6....6....6...6..6..6.6........
.0..3...17....26...27...27..27.27.27..........
.0..0...35....84...98...99..99.99.............
.0..4..102...324..442..462.463................
.0..0..240..1170.1968.2205....................
.0..0..665..4412.9214.........................
.0.11.1661.16313..............................
.0.12.4501....................................
.0.13.........................................
.0............................................

Column 2 (ternary square free words reduced by similarity) comes out

 1 1 1 2 0 3 0 4 0 0 11 12 13 0 5 8 0 42 38 50 7 77 115 120 125

which has some structure that might be analyzable.

 rhhardin at mindspring.com
rhhardin at att.net (either)