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

%I A256456 #43 Jul 08 2016 00:10:40
%S A256456 0,1,1,4,8,29,79,280,912,3260,11410,41272,148976,544802,1997499,
%T A256456 7372080,27299360,101520714,378721134,1417339352,5318837680,
%U A256456 20012141478,75473438326,285268537424,1080433781728,4099860518208,15585111068644,59343308199216,226312777319776
%N A256456 Number of simple 2n-gons with only right angles, disregarding edge lengths.
%C A256456 a(n) is also the number of bracelets containing n+2 R's and n-2 L's.
%C A256456 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
%H A256456 Bjarki Ágúst Guðmundsson, <a href="/A256456/b256456.txt">Table of n, a(n) for n = 1..100</a> [Terms 1 through 30 were computed by Brent A. Yorgey; and terms 31 to 100 by _Bjarki Ágúst Guðmundsson_, Jul 07 2016]
%H A256456 Mark Jason Dominus, <a href="/A256456/a256456.png">Examples of the a(5)=8 orthogonal decagons; also bracelets of 7 R's and 3 L's</a>
%H A256456 Mark Dominus, <a href="http://plover.com/~mjd/misc/math/polygons/enumerate-orthogonal-polygons">Perl program</a>
%H A256456 Brent Yorgey, <a href="https://github.com/byorgey/ortho-polys/blob/master/BraceletCI.hs">Haskell program</a>
%e A256456 For n=5 the a(5)=8 bracelets are RRRLRRLRRL, RRRLRRRLRL, RRRRLRRLRL, RRRRLRRRLL, RRRRRLRLRL, RRRRRLRRLL, RRRRRRLRLL, RRRRRRRLLL.
%t A256456 {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 *)
%K A256456 nonn
%O A256456 1,4
%A A256456 _Mark Jason Dominus_, Mar 29 2015
%E A256456 Corrected (a(14) was wrong) and extended by _Brent A. Yorgey_, Dec 11 2015
%E A256456 a(31)-a(100) from _Bjarki Ágúst Guðmundsson_, Jul 07 2016