

A256456


Number of simple 2ngons 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
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OFFSET

1,4


COMMENTS

a(n) is also the number of bracelets containing n+2 R's and n2 L's.
This is also the number of bracelets of n2 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



