[seqfan] Re: Number of k-divided sequences (corrected)

[Richard Mathar]

http://list.seqfan.eu/pipermail/seqfan/2012-March/016590.html

njas> From seqfan-bounces at list.seqfan.eu Mon Mar 19 18:00:48 2012
njas> To: seqfan at list.seqfan.eu
njas> Subject: [seqfan] Number of k-divided sequences (corrected)
njas> 
njas> A sequence (or string, or word) S of length n
njas> with entries from A is called "k-divided over A" if
njas> you can write it as
njas> S = U_1 U_2 ... U_k
njas> with the property that for any nontrivial permutation
njas> pi of {1..k} we have
njas> 
njas> S < U_pi_1 U_pi_2 ... U_pi_k

I have compared A209970, A210109 , A210323 (2 or 3 letters with k=2 or k=3) for 
words of length n <=17 with my program and the counts match.
Further results predicted as follows:

base 2 k 2
2 1
3 4
4 10
5 24
6 50
7 108
8 220
9 452
10 916
11 1860
12 3744
13 7560
14 15202
base 2 k 3
2 0
3 0
4 2
5 7
6 23
7 54
8 132
9 290
10 634
11 1342
12 2834
13 5868
14 12140
base 2 k 4
2 0
3 0
4 0
5 0
6 1
7 11
8 37
9 109
10 287
base 2 k 5
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 6
10 36
base 2 k 6
2 0
3 0
4 0
5 0
6 0
7 0
8 0
9 0
10 0
base 3 k 2
2 3
3 16
4 57
5 192
6 599
7 1872
8 5727
9 17488
10 53115
11 161040
12 487073
13 1471680
14 4441167
base 3 k 3
2 0
3 1
4 16
5 78
6 324
7 1141
8 3885
9 12630
10 40315
11 126604
12 393986
base 3 k 4
2 0
3 0
4 0
5 6
6 56
7 343
8 1534
9 6067
10 22162
base 3 k 5
2 0
3 0
4 0
5 0
6 0
7 15
8 166
9 1135
10 5865

base 4 k 2
2 6
3 40
4 186
5 816
6 3396
7 14040
8 57306
9 233000
10 943608
base 4 k 3
2 0
3 4
4 60
5 374
6 1960
7 9103
8 40497
9 174127
10 735268
base 4 k 4
2 0
3 0
4 1
5 44
6 450
7 3175
8 17977