A127685 Number of non-isomorphic maximal independent sets of the n-cycle graph.

0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 3, 5, 5, 7, 6, 10, 9, 14, 14, 20, 20, 30, 31, 44, 48, 67, 74, 104, 117, 161, 188, 254, 302, 407, 489, 654, 801, 1064, 1315, 1742, 2174, 2867, 3613, 4747, 6019, 7900, 10069, 13190, 16895, 22103, 28413, 37150, 47900, 62590, 80912

Offset

1,6

Comments

Number of non-isomorphic (i.e. defined up to a rotation and a reflection) maximal independent sets of the n-cycle graph. Also: Number of cyclic compositions of n in which each term is either 2 or 3, where a clockwise writing is not distinguished from its counterclockwise counterpart.

References

R. Bisdorff and J.-L. Marichal, Counting non-isomorphic maximal independent sets of the n-cycle graph, ar2007.

Links

Table of n, a(n) for n=1..57.

R. Bisdorff and J.-L. Marichal, Counting non-isomorphic maximal independent sets of the n-cycle graph, arXiv:0701647 (2007) and JIS 11 (2008) 08.5.7.

Formula

a(n) = A127682(n) + Sum(d divides n) A127683(d) = (1/2)*(A127682(n) + (1/n)*(Sum(d divides n) A000010(n/d) A001608(d)))

Crossrefs

Cf. A127682, A127683, A001608.

Sequence in context: A053267 A058768 A127682 * A127687 A024156 A241316

Adjacent sequences: A127682 A127683 A127684 * A127686 A127687 A127688

Keyword

easy,nonn

Author

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

Status

approved