Family of fractal sequences

[Kerry Mitchell]

Just submitted to OEIS:

Let A be the sequence A114729 (1, 1, 1, 2, 3, 2, 2, 1, 1, 1, 2, 3, 4,
4, 3, 3, 2, 2, 1, 1, ...), B be the sequence A114730 (1, 1, 2, 2, 1,
1, 1, 2, 3, 4, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, ...), and C be the
sequence A114731 (1, 2, 1, 1, 1, 2, 3, 3, 2, 2, 1, 1, 1, 2, 3, 4, 5,
4, 4, 3, ...).  Let D be the sequence A114732 (1, 2, 3, 1, 1, 2, 3, 4,
5, 6, 4, 2, 1, 2, 3, 4, 5, 6, 7, 8, ...), E be the sequence A114733
(1, 2, 1, 2, 3, 4, 5, 3, 1, 1, 2, 3, 4, 5, 6, 7, 8, 6, 4, 2, ...), and
F be the sequence A114734 (1, 1, 2, 3, 4, 2, 1, 2, 3, 4, 5, 6, 7, 5,
3, 1, 1, 2, 3, 4, ...).  Then:

- A upper trims to B
- B upper trims to C
- C upper trims to A
- A lower trims to C
- B lower trims to A
- C lower trims to B
- D counts the number of times each element of A occurs
- E counts the number of times each element of B occurs
- F counts the number of times each element of C occurs
- A counts the number of times each element of D occurs
- B counts the number of times each element of E occurs
- C counts the number of times each element of F occurs
- D lower trims to E
- E lower trims to F
- F lower trims to D
- D upper trims to F
- E upper trims to D
- F upper trims to E

Kerry