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%I #14 Mar 17 2024 05:55:21
%S 1,1,3,2,6,1,6,1,5,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,
%T 4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,
%U 4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4,1,4
%N Number of maximal vertex-independent sets in the hypergraph with nodes V = {1, 2, ..., n} and "edges" consisting of the triples (X,Y,Z) with X<Y<Z and X+Y=Z.
%C A subset S of V is vertex-independent if there is no edge (X,Y,Z) with X, Y, Z all in S.
%C Continued fraction expansion of (3452449 + 2*sqrt(2))/1943849. - _Stefano Spezia_, Mar 17 2024
%H J. Sedláček, <a href="https://doi.org/10.1111/j.1749-6632.1970.tb56488.x">On a set system</a>, Annals New York Acad. Sci., 175 (No. 1, 1970), 329-330.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F a(2k)=1, a(2k+1)=4 for k >= 5.
%F G.f.: x*(1 + x + 2*x^2 + x^3 + 3*x^4 - x^5 - x^8 - x^10)/((1 - x)*(1 + x)). - _Stefano Spezia_, Mar 17 2024
%Y Cf. A002848, A002849, A108235.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_, Feb 10 2010
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