A256456 Number of simple 2n-gons with only right angles, disregarding edge lengths.

0, 1, 1, 4, 8, 29, 79, 280, 912, 3260, 11410, 41272, 148976, 544802, 1997499, 7372080, 27299360, 101520714, 378721134, 1417339352, 5318837680, 20012141478, 75473438326, 285268537424, 1080433781728, 4099860518208, 15585111068644, 59343308199216, 226312777319776

Offset: 1

Author

Mark Jason Dominus, Mar 29 2015

Keywords

• nonn

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

Examples

			For n=5 the a(5)=8 bracelets are RRRLRRLRRL, RRRLRRRLRL, RRRRLRRLRL, RRRRLRRRLL, RRRRRLRLRL, RRRRRLRRLL, RRRRRRLRLL, RRRRRRRLLL.
		

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

Programs

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 *)

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