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A324946 Number of cyclic change-ringing sequences of length n for 6 bells.

%I A324946 #25 Jul 25 2019 04:34:03
%S A324946 1,12,60,364,2040,11640,75572,584306,5025774,44468794,392052540,
%T A324946 3439315382,30250738752
%N A324946 Number of cyclic change-ringing sequences of length n for 6 bells.
%C A324946 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:
%C A324946 1. The position of each bell (number) from one permutation to the next can stay the same or move by at most one place.
%C A324946 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.
%C A324946 3. The sequence must start with the permutation (1,2,3,4,5,6).
%C A324946 4. The sequence must end with the same permutation that it started with.
%C A324946 [*]: We define the length of a change-ringing sequence to be the number of permutations in the sequence.
%C A324946 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 cyclic change-ringing sequences of length n for m bells as a_m(n), {a_m(n)} has factorial(m) terms for all m.
%H A324946 Jonas K. Sønsteby, <a href="https://github.com/jonassonsteby/change-ringing">Python program</a>.
%H A324946 <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>
%o A324946 (Python 3.7) See Jonas K. Sønsteby link.
%Y A324946 4 bells: A324942, A324943.
%Y A324946 5 bells: A324944, A324945.
%Y A324946 6 bells: This sequence, A324947.
%Y A324946 7 bells: A324948, A324949.
%Y A324946 8 bells: A324950, A324951.
%Y A324946 9 bells: A324952, A324953.
%Y A324946 Number of allowable transition rules: A000071.
%K A324946 nonn,fini,more
%O A324946 1,2
%A A324946 _Jonas K. Sønsteby_, Mar 20 2019
%E A324946 a(8)-a(13) from _Bert Dobbelaere_, Jul 25 2019