A127682 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.

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, 49, 37, 65, 49, 86, 65, 114, 86, 151, 114, 200, 151, 265, 200, 351, 265, 465, 351, 616, 465, 816, 616, 1081, 816, 1432, 1081, 1897, 1432, 2513, 1897, 3329, 2513, 4410, 3329

Offset: 1

Author

Jean-Luc Marichal (jean-luc.marichal(AT)uni.lu), Jan 24 2007

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• R. Bisdorff and J.-L. Marichal, Counting non-isomorphic maximal independent sets of the n-cycle graph, arXiv:math/0701647 [math.CO], 2007-2008 and JIS 11 (2008) 08.5.7.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,1).

Crossrefs

Cf. A000931.

Programs

Mathematica

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 *)
LinearRecurrence[{0,0,0,1,0,1},{0,1,1,1,1,2},70] (* Harvey P. Dale, Jul 17 2014 *)

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

Formula

a(n) = A000931(k+3) if n=2k-1 and a(n) = A000931(k+5) if n=2k.

a(n) = a(n-4) + a(n-6).

G.f.: -x^2*(x^4+x^3+x^2+x+1) / (x^6+x^4-1). - Colin Barker, Mar 29 2014