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 A165964 #18 Jul 07 2025 20:18:04
%S A165964 1,1,0,4,16,86,542,3932,32330,297438,3028320,33814454,410954878,
%T A165964 5400878692,76329470882,1154445436334,18606430004984,318369275913710,
%U A165964 5764046146341198,110091446931897180,2212282487296335866,46658484076867264702,1030533208360458081232
%N A165964 Number of circular permutations of length n without increasing or decreasing 3-sequences.
%C A165964 Circular permutations are permutations whose indices are from the ring of integers modulo n. Increasing 3-sequences are of the form i,i+1,i+2, while decreasing 3-sequences are of the form i,i-1,i-2.
%H A165964 Alois P. Heinz, <a href="/A165964/b165964.txt">Table of n, a(n) for n = 1..450</a>
%H A165964 W. M. Dymacek, I. Lambert, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Dymacek/dymacek5.html">Permutations Avoiding Runs of i, i+1, i+2 or i, i-1, i-2 </a>, J. Int. Seq. 14 (2011) # 11.1.6, Table 1.
%F A165964 a(n) = A095816(n-1) - 2 * Sum_{i=1..[(n+1)/3]} (A095816(n-3*i) - A095816(n-1-3*i)). [Corrected by _Sean A. Irvine_, Jul 07 2025]
%e A165964 For n=4 the a(4)=4 solutions are (0,1,3,2), (0,2,1,3), (0,2,3,1), and (0,3,1,2).
%Y A165964 Cf. A095816, A165963, A078628.
%K A165964 nonn
%O A165964 1,4
%A A165964 _Isaac Lambert_, Oct 07 2009
%E A165964 Edited and more terms added by _Max Alekseyev_, Jun 14 2011