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A324947 Number of path change-ringing sequences of length n for 6 bells. 11
1, 12, 132, 1392, 14348, 146424, 1488108, 15083740, 152484278, 1537437464, 15465605806, 155275855726, 1556493430588 (list; graph; refs; listen; history; text; internal format)
a(n) is the number of (change-ringing) sequences of length[*] n when we are looking at sequences of permutations of the set {1,2,3,4,5,6} that satisfy:
1. The position of each bell (number) from one permutation to the next can stay the same or move by at most one place.
2. No permutation can be repeated except for the starting permutation which can be repeated at most once at the end of the sequence to accommodate criterion 4.
3. The sequence must start with the permutation (1,2,3,4,5,6).
And does not satisfy:
4. The sequence must end with the same permutation that it started with.
[*]: We define the length of a change-ringing sequence to be the number of permutations in the sequence.
With this [*] definition of the length of a change-ringing sequence; for 6 bells we get a maximum length of factorial(6)=720, thus we have 720 possible lengths, namely 1,2,...,720. Hence {a(n)} has 720 terms. For m bells, where m is a natural number larger than zero, we get a maximum length of factorial(m). When denoting the number of path change-ringing sequences of length n for m bells as a_m(n), {a_m(n)} has factorial(m) terms for all m.
Jonas K. Sønsteby, Python program.
(Python 3.7) See Jonas K. Sønsteby link.
4 bells: A324942, A324943.
5 bells: A324944, A324945.
6 bells: A324946, this sequence.
7 bells: A324948, A324949.
8 bells: A324950, A324951.
9 bells: A324952, A324953.
Number of allowable transition rules: A000071.
Sequence in context: A125447 A162767 A003495 * A165150 A002921 A199941
_Jonas K. Sønsteby_, Mar 20 2019
a(8)-a(13) from _Bert Dobbelaere_, Jul 25 2019

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Last modified February 29 20:48 EST 2024. Contains 370428 sequences. (Running on oeis4.)