A007388 5th-order maximal independent sets in cycle graph.

0, 2, 3, 2, 5, 2, 7, 2, 9, 2, 11, 2, 13, 9, 15, 18, 17, 29, 19, 42, 28, 57, 46, 74, 75, 93, 117, 121, 174, 167, 248, 242, 341, 359, 462, 533, 629, 781, 871, 1122, 1230, 1584, 1763, 2213, 2544, 3084, 3666, 4314, 5250, 6077, 7463, 8621, 10547

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, J. Graph Theory, submitted, 1994, apparently unpublished.

Links

• R. Yanco, Letter and Email to N. J. A. Sloane, 1994
• R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994. (Annotated scanned copy)

Crossrefs

Cf. A001608, A007387, A007389.

Formula

Empirical g.f.: x^2*(5*x^10+3*x^8-2*x^5-2*x^3-3*x-2) / (x^7+x^2-1). - Colin Barker, Mar 29 2014

For n >= 13: a(n) = a(n-2) + a(n-7). - Sean A. Irvine, Jan 02 2018

a(n) = Sum_{j=0..floor((n-g)/(2*g))} (2*n/(n-2*(g-2)*j-(g-2))) * Hypergeometric2F1([-(n-2g*j-g)/2,-(2j+1)], [1], 1), g = 7, n >= g and n an odd integer. - Richard Turk, Oct 14 2019

Extensions

Typo in data (242 was inadvertently repeated) fixed by Colin Barker, Mar 29 2014

More terms from Sean A. Irvine, Jan 02 2018