The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238937 The number of squarefree permutations of 1,...,n up to symmetry. 2


%S 1,1,2,3,10,26,105,278,1011,3804,17065,78012,406795,2192844,13318687,

%T 79804728,533838106

%N The number of squarefree permutations of 1,...,n up to symmetry.

%C A permutation is squarefree if it does not contain two consecutive factors of length two or more that are in the same relative order. For example, the permutation 243156 is squarefree, while the permutation 631425 contains the square 3142 (indeed, 31 is order-isomorphic to 42). Squarefree permutations exist of any length, and their numbers are given in the sequence A221989.

%C This sequence gives the number of squarefree permutations of 1,...,n up to symmetry. There are two kinds of symmetries involved: the reverse of a permutation s = i_1 i_2 ... i_n is the permutation r(s) = i_n ... i_2 i_1, and the complement of s is the permutation c(s) = (n+1-i_1) (n+1-i_2) ... (n+1-i_n). "Up to symmetry" means that if a permutation s has been already counted, then c(s), r(s) and c(r(s))=r(c(s)) are not counted.

%H Ian Gent, Sergey Kitaev, Alexander Konovalov, Steve Linton and Peter Nightingale, <a href="http://arxiv.org/abs/1402.3582">S-crucial and bicrucial permutations with respect to squares</a>, arXiv:1402.3582, 2014 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Kitaev/kitaev10.html">J. Int. Seq. 18 (2015) 15.6.5</a> .

%F For n>2, A221989(n) = 4*a(n) - 2*A238942(n).

%Y Cf. A221989, A238942.

%K nonn,more

%O 1,3

%A _Alexander Konovalov_ et al., Mar 07 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 23 04:16 EST 2020. Contains 331168 sequences. (Running on oeis4.)