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 A165964 Number of circular permutations of length n without increasing or decreasing 3-sequences. 11

%I

%S 1,1,0,4,16,86,542,3932,32330,297438,3028320,33814454,410954878,

%T 5400878692,76329470882,1154445436334,18606430004984,318369275913710,

%U 5764046146341198,110091446931897180,2212282487296335866

%N Number of circular permutations of length n without increasing or decreasing 3-sequences.

%C 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 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 a(n) = A095816(n-1) - 2 * Sum{i=1,[n/3], A095816(n-3i) - A095816(n-1-3i)}.

%e 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 Cf. A095816, A165963, A078628.

%K nonn

%O 1,4

%A _Isaac Lambert_, Oct 07 2009

%E Edited and more terms added by _Max Alekseyev_, Jun 14 2011

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Last modified August 17 23:13 EDT 2022. Contains 356204 sequences. (Running on oeis4.)