OFFSET
1,4
COMMENTS
a(n) is also the number of bracelets containing n+2 R's and n-2 L's.
This is also the number of bracelets of n-2 nonnegative integers whose sum is n+2; this explains the labels on the decagons in the illustration. - Mark Jason Dominus, Jun 08 2015
LINKS
Bjarki Ágúst Guðmundsson, Table of n, a(n) for n = 1..100 [Terms 1 through 30 were computed by Brent A. Yorgey; and terms 31 to 100 by Bjarki Ágúst Guðmundsson, Jul 07 2016]
Mark Jason Dominus, Examples of the a(5)=8 orthogonal decagons; also bracelets of 7 R's and 3 L's
Mark Dominus, Perl program
Brent Yorgey, Haskell program
EXAMPLE
For n=5 the a(5)=8 bracelets are RRRLRRLRRL, RRRLRRRLRL, RRRRLRRLRL, RRRRLRRRLL, RRRRRLRLRL, RRRRRLRRLL, RRRRRRLRLL, RRRRRRRLLL.
MATHEMATICA
{0}~Join~Table[Coefficient[CycleIndexPolynomial[DihedralGroup[2n], Table[1+t^i, {i, 1, 2n}]], t^(n+2)], {n, 2, 30}] (* Bjarki Ágúst Guðmundsson, Jul 07 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Mark Jason Dominus, Mar 29 2015
EXTENSIONS
Corrected (a(14) was wrong) and extended by Brent A. Yorgey, Dec 11 2015
a(31)-a(100) from Bjarki Ágúst Guðmundsson, Jul 07 2016
STATUS
approved