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

1,4

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

Sequence in context: A280085 A322784 A297638 * A270522 A317583 A020331

Adjacent sequences: A256453 A256454 A256455 * A256457 A256458 A256459

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