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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

Table of n, a(n) for n=1..21.

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 * A005618 A005495 A052124

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 November 26 13:30 EST 2014. Contains 250079 sequences.