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 A165964 Number of circular permutations of length n without increasing or decreasing 3-sequences. 11
 1, 1, 0, 4, 16, 86, 542, 3932, 32330, 297438, 3028320, 33814454, 410954878, 5400878692, 76329470882, 1154445436334, 18606430004984, 318369275913710, 5764046146341198, 110091446931897180, 2212282487296335866 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. LINKS W. M. Dymacek, I. Lambert, Permutations Avoiding Runs of i, i+1, i+2 or i, i-1, i-2 , J. Int. Seq. 14 (2011) # 11.1.6, Table 1. FORMULA a(n) = A095816(n-1) - 2 * Sum{i=1,[n/3], A095816(n-3i) - A095816(n-1-3i)}. EXAMPLE 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). CROSSREFS Cf. A095816, A165963, A078628. Sequence in context: A074876 A238722 A184507 * A300279 A321238 A005618 Adjacent sequences:  A165961 A165962 A165963 * A165965 A165966 A165967 KEYWORD nonn AUTHOR Isaac Lambert, Oct 07 2009 EXTENSIONS Edited and more terms added by Max Alekseyev, Jun 14 2011 STATUS approved

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Last modified July 5 05:47 EDT 2022. Contains 355087 sequences. (Running on oeis4.)