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 A324951 #13 May 17 2025 09:54:58
%S A324951 1,33,1056,33384,1048280,32797176,1023968632,31928050304,994658931028
%N A324951 Number of path change-ringing sequences of length n for 8 bells.
%C A324951 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} that satisfy:
%C A324951 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 A324951 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 A324951 3. The sequence must start with the permutation (1,2,3,4,5,6,7,8).
%C A324951 And does not satisfy:
%C A324951 4. The sequence must end with the same permutation that it started with.
%C A324951 [*]: We define the length of a change-ringing sequence to be the number of permutations in the sequence.
%C A324951 With this [*] definition of the length of a change-ringing sequence; for 8 bells we get a maximum length of factorial(8)=40320, thus we have 40320 possible lengths, namely 1,2,...,40320. Hence {a(n)} has 40320 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.
%H A324951 Jonas K. Sønsteby, <a href="https://github.com/jonassonsteby/change-ringing">Python program</a>.
%H A324951 <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>.
%o A324951 (Python 3.7) # See Jonas K. Sønsteby link.
%Y A324951 4 bells: A324942, A324943.
%Y A324951 5 bells: A324944, A324945.
%Y A324951 6 bells: A324946, A324947.
%Y A324951 7 bells: A324948, A324949.
%Y A324951 8 bells: A324950, This sequence.
%Y A324951 9 bells: A324952, A324953.
%Y A324951 Number of allowable transition rules: A000071.
%K A324951 nonn,fini,more
%O A324951 1,2
%A A324951 _Jonas K. Sønsteby_, May 01 2019
%E A324951 a(7)-a(9) from _Bert Dobbelaere_, May 17 2025