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A256456 Number of simple 2n-gons with only right angles, disregarding edge lengths. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A025234 A075308 A280085 * A270522 A020331 A248476

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

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Last modified March 28 12:08 EDT 2017. Contains 284186 sequences.