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A324947 Number of path change-ringing sequences of length n for 6 bells.

%I A324947 #25 Jul 25 2019 07:02:21
%S A324947 1,12,132,1392,14348,146424,1488108,15083740,152484278,1537437464,
%T A324947 15465605806,155275855726,1556493430588
%N A324947 Number of path change-ringing sequences of length n for 6 bells.
%C A324947 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 A324947 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 A324947 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 A324947 3. The sequence must start with the permutation (1,2,3,4,5,6).
%C A324947 And does not satisfy:
%C A324947 4. The sequence must end with the same permutation that it started with.
%C A324947 [*]: We define the length of a change-ringing sequence to be the number of permutations in the sequence.
%C A324947 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.
%H A324947 Jonas K. Sønsteby, <a href="https://github.com/jonassonsteby/change-ringing">Python program</a>.
%H A324947 <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>
%o A324947 (Python 3.7) See Jonas K. Sønsteby link.
%Y A324947 4 bells: A324942, A324943.
%Y A324947 5 bells: A324944, A324945.
%Y A324947 6 bells: A324946, this sequence.
%Y A324947 7 bells: A324948, A324949.
%Y A324947 8 bells: A324950, A324951.
%Y A324947 9 bells: A324952, A324953.
%Y A324947 Number of allowable transition rules: A000071.
%K A324947 nonn,fini,more
%O A324947 1,2
%A A324947 _Jonas K. Sønsteby_, Mar 20 2019
%E A324947 a(8)-a(13) from _Bert Dobbelaere_, Jul 25 2019