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

Author

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

Keywords

• easy
• nonn

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

• 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.

Crossrefs

Cf. A127682, A127683, A001608.

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)))