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 A007974 #31 Apr 12 2025 16:52:07 %S A007974 1,6,52,389,2539,16604,105365,654030,3900116,22073230,116855950, %T A007974 567965207 %N A007974 Number of permutations that are n-3 "block reversals" away from 12...n. %F A007974 a(n) = A300003(n,n-3). %o A007974 (Python) %o A007974 def a(n): %o A007974 perm = tuple(range(1, n+1)); reach = {perm}; frontier = {perm} %o A007974 for k in range(n-3): %o A007974 r1 = set() %o A007974 while len(frontier) > 0: %o A007974 q = frontier.pop() %o A007974 for i in range(n): %o A007974 for j in range(i+1, n+1): %o A007974 qp = list(q) %o A007974 qp[i:j] = qp[i:j][::-1] %o A007974 qp = tuple(qp) %o A007974 if qp not in reach: %o A007974 reach.add(qp) %o A007974 r1.add(qp) %o A007974 frontier = r1 %o A007974 return len(frontier) %o A007974 print([a(n) for n in range(3, 10)]) # _Michael S. Branicky_, Jan 26 2023 %Y A007974 Cf. A007972, A007973, A007975, A300003. %K A007974 nonn,more %O A007974 3,2 %A A007974 _J. H. Conway_ %E A007974 a(9)-a(11) from _Sean A. Irvine_, Feb 22 2018 %E A007974 a(12) from _Thomas Baruchel_, Mar 26 2025 %E A007974 a(13)-a(14) from _Bert Dobbelaere_, Apr 12 2025