A007388 5th-order maximal independent sets in cycle graph. (Formerly M0425)

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

1,2

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A. Bagchi, K-th order maximal independent sets in path and cycle graphs, J. Graph Theory, submitted, 1994, apparently unpublished.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

Table of n, a(n) for n=1..53.

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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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)

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

Crossrefs

Cf. A001608, A007387, A007389.

Sequence in context: A248737 A141310 A007389 * A348846 A057815 A007387

Adjacent sequences: A007385 A007386 A007387 * A007389 A007390 A007391

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Extensions

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

More terms from Sean A. Irvine, Jan 02 2018

Status

approved