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A007389 7th-order maximal independent sets in cycle graph.
(Formerly M0424)
4
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 (list; graph; refs; listen; history; text; internal format)
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A. Bagchi, K-th order maximal independent sets in path and cycle graphs, J. Graph Theory, submitted, 1994, apparently unpublished.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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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 A057815 A007387

Adjacent sequences:  A007386 A007387 A007388 * A007390 A007391 A007392

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified June 24 05:58 EDT 2021. Contains 345416 sequences. (Running on oeis4.)