login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A303117 a(n) is the number of cyclic permutations with at most two descents. 1
1, 1, 1, 2, 6, 18, 62, 186, 570, 1680, 4890, 14058, 40200, 114450, 325230, 923846, 2624730, 7465410, 21260652, 60647370, 173288724, 496014934, 1422211494, 4084793082, 11751102060, 33857989968, 97696908330, 282295318536, 816759712080, 2366027865810, 6861963548198, 19922800783578, 57902584654650 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
The number of cyclic permutations with at most 2 descents is equal to L(3,n)-n*L(2,n) where L(k,n) is the number of primitive necklaces (equivalently, the number of Lyndon words) of length n on k letters.
LINKS
I. M. Gessel and C. Reutenauer, Counting permutations with given cycle structure and descent set, J. Combin. Theory, Ser. A, 64, 189-215, (1993).
FORMULA
a(n) = A027376(n) - n*A001037(n).
a(n) = L(3,n)-n*L(2,n) where L(k,n) is the number of primitive k-ary necklaces (or equivalently, Lyndon words) of length n.
PROG
(PARI) L2(n) = if(n>1, sumdiv(n, d, moebius(d)*2^(n/d))/n, n+1); \\ A001037
L3(n) = if(n<1, n==0, sumdiv(n, d, moebius(n/d)*3^d)/n); \\ A027376
a(n) = L3(n)-n*L2(n); \\ Michel Marcus, May 17 2018
CROSSREFS
Sequence in context: A346490 A177473 A177471 * A150052 A262590 A150053
KEYWORD
nonn
AUTHOR
Kassie Archer, Apr 18 2018
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 03:54 EDT 2024. Contains 373540 sequences. (Running on oeis4.)