This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324952 #13 May 17 2025 09:55:02
%S A324952 1,54,996,28884,834680,26371654,885870328,31508181992,1175640098592
%N A324952 Number of cyclic change-ringing sequences of length n for 9 bells.
%C A324952 a(n) is the number of (change-ringing) sequences of length[*] n when we are looking at sequences of permutations of the set {1,2,3,4,5,6,7,8,9} that satisfy:
%C A324952 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 A324952 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 A324952 3. The sequence must start with the permutation (1,2,3,4,5,6,7,8,9).
%C A324952 4. The sequence must end with the same permutation that it started with.
%C A324952 [*]: We define the length of a change-ringing sequence to be the number of permutations in the sequence.
%C A324952 With this [*] definition of the length of a change-ringing sequence; for 9 bells we get a maximum length of factorial(9)=362880, thus we have 362880 possible lengths, namely 1,2,...,362880. Hence {a(n)} has 362880 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 A324952 Jonas K. Sønsteby, <a href="https://github.com/jonassonsteby/change-ringing">Python program</a>.
%H A324952 <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>.
%o A324952 (Python 3.7) # See Jonas K. Sønsteby link.
%Y A324952 4 bells: A324942, A324943.
%Y A324952 5 bells: A324944, A324945.
%Y A324952 6 bells: A324946, A324947.
%Y A324952 7 bells: A324948, A324949.
%Y A324952 8 bells: A324950, A324951.
%Y A324952 9 bells: This sequence, A324953.
%Y A324952 Number of allowable transition rules: A000071.
%K A324952 nonn,fini,more
%O A324952 1,2
%A A324952 _Jonas K. Sønsteby_, May 01 2019
%E A324952 a(6)-a(9) from _Bert Dobbelaere_, May 17 2025