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%I M0424 #42 Nov 22 2019 13:17:43
%S 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,
%T 86,58,107,93,130,143,155,210,191,296,249,403,342,533,485,688,695,879,
%U 991,1128,1394,1470,1927,1955,2615,2650,3494,3641,4622,5035,6092,6962,8047
%N 7th-order maximal independent sets in cycle graph.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, J. Graph Theory, submitted, 1994, apparently unpublished.
%H Richard Turk, <a href="/A007389/a007389.txt">Notes on proposed formula</a>
%H R. Yanco, <a href="/A007380/a007380.pdf">Letter and Email to N. J. A. Sloane, 1994</a>
%H R. Yanco and A. Bagchi, <a href="/A007380/a007380_1.pdf">K-th order maximal independent sets in path and cycle graphs</a>, Unpublished manuscript, 1994. (Annotated scanned copy)
%F 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
%F 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.
%Y Cf. A001608, A007387, A007388.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Mira Bernstein_