%I #23 Mar 19 2024 08:30:20
%S 0,1,1,1,1,2,1,2,2,3,2,4,3,5,4,7,5,9,7,12,9,16,12,21,16,28,21,37,28,
%T 49,37,65,49,86,65,114,86,151,114,200,151,265,200,351,265,465,351,616,
%U 465,816,616,1081,816,1432,1081,1897,1432,2513,1897,3329,2513,4410,3329
%N Number of non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets of the n-cycle graph having at least one symmetry axis. Also: Number of cyclic and palindromic compositions of n in which each term is either 2 or 3.
%H Vincenzo Librandi, <a href="/A127682/b127682.txt">Table of n, a(n) for n = 1..1000</a>
%H R. Bisdorff and J.-L. Marichal, <a href="https://arxiv.org/abs/math/0701647">Counting non-isomorphic maximal independent sets of the n-cycle graph</a>, arXiv:math/0701647 [math.CO], 2007-2008 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Marichal/marichal.html">JIS 11 (2008) 08.5.7</a>.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,1).
%F a(n) = A000931(k+3) if n=2k-1 and a(n) = A000931(k+5) if n=2k.
%F a(n) = a(n-4) + a(n-6).
%F G.f.: -x^2*(x^4+x^3+x^2+x+1) / (x^6+x^4-1). - _Colin Barker_, Mar 29 2014
%t Rest[CoefficientList[Series[-x^2*(x^4+x^3+x^2+x+1)/(x^6+x^4-1),{x,0,63}],x]] (* _Vaclav Kotesovec_, Mar 29 2014 *)
%t LinearRecurrence[{0,0,0,1,0,1},{0,1,1,1,1,2},70] (* _Harvey P. Dale_, Jul 17 2014 *)
%o (PARI) concat(0, Vec(-x^2*(x^4+x^3+x^2+x+1)/(x^6+x^4-1) + O(x^100))) \\ _Colin Barker_, Mar 29 2014
%Y Cf. A000931.
%K easy,nonn
%O 1,6
%A Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007