login
A161826
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.
3
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, 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, 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
OFFSET
1,3
COMMENTS
A subset S of V is vertex-independent if there is no edge (X,Y,Z) with X, Y, Z all in S.
Continued fraction expansion of (3452449 + 2*sqrt(2))/1943849. - Stefano Spezia, Mar 17 2024
LINKS
J. Sedláček, On a set system, Annals New York Acad. Sci., 175 (No. 1, 1970), 329-330.
FORMULA
a(2k)=1, a(2k+1)=4 for k >= 5.
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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 10 2010
STATUS
approved