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