

A127682


Number of nonisomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets of the ncycle 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.


6



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
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OFFSET

1,6


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
R. Bisdorff and J.L. Marichal, Counting nonisomorphic maximal independent sets of the ncycle graph, arXiv:070164 (2007) and JIS 11 (2008) 08.5.7.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,1).


FORMULA

a(n) = A000931(k+3) if n=2k1 and a(n) = A000931(k+5) if n=2k.
a(n) = a(n4) + a(n6).
G.f.: x^2*(x^4+x^3+x^2+x+1) / (x^6+x^41).  Colin Barker, Mar 29 2014


MATHEMATICA

Rest[CoefficientList[Series[x^2*(x^4+x^3+x^2+x+1)/(x^6+x^41), {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 *)


PROG

(PARI) concat(0, Vec(x^2*(x^4+x^3+x^2+x+1)/(x^6+x^41) + O(x^100))) \\ Colin Barker, Mar 29 2014


CROSSREFS

Cf. A000931.
Sequence in context: A282537 A053267 A058768 * A127685 A127687 A024156
Adjacent sequences: A127679 A127680 A127681 * A127683 A127684 A127685


KEYWORD

easy,nonn


AUTHOR

JeanLuc Marichal (jeanluc.marichal(AT)uni.lu), Jan 24 2007


STATUS

approved



