

A165964


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


11



1, 1, 0, 4, 16, 86, 542, 3932, 32330, 297438, 3028320, 33814454, 410954878, 5400878692, 76329470882, 1154445436334, 18606430004984, 318369275913710, 5764046146341198, 110091446931897180, 2212282487296335866
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OFFSET

1,4


COMMENTS

Circular permutations are permutations whose indices are from the ring of integers modulo n. Increasing 3sequences are of the form i,i+1,i+2, while decreasing 3sequences are of the form i,i1,i2.


LINKS

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


FORMULA

a(n) = A095816(n1)  2 * Sum{i=1,[n/3], A095816(n3i)  A095816(n13i)}.


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



