A007389 7th-order maximal independent sets in cycle graph. (Formerly M0424)

0, 2, 3, 2, 5, 2, 7, 2, 9, 2, 11, 2, 13, 2, 15, 2, 17, 11, 19, 22, 21, 35, 23, 50, 25, 67, 36, 86, 58, 107, 93, 130, 143, 155, 210, 191, 296, 249, 403, 342, 533, 485, 688, 695, 879, 991, 1128, 1394, 1470, 1927, 1955, 2615, 2650, 3494, 3641, 4622, 5035, 6092, 6962, 8047

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A. Bagchi, K-th order maximal independent sets in path and cycle graphs, J. Graph Theory, submitted, 1994, apparently unpublished.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..60.

Richard Turk, Notes on proposed formula

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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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*(7*x^14 + 5*x^12 + 3*x^10 - 2*x^7 - 2*x^5 - 2*x^3 - 3*x - 2) / (x^9 + x^2 - 1). - Colin Barker, Mar 29 2014

Theorem: 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 = 9, n >= g and n an odd integer. - Richard Turk, Oct 14 2019 For proof see attached text file.

Crossrefs

Cf. A001608, A007387, A007388.

Sequence in context: A108077 A248737 A141310 * A007388 A348846 A057815

Adjacent sequences: A007386 A007387 A007388 * A007390 A007391 A007392

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein

Status

approved