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.

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

Table of n, a(n) for n=1..99.

J. Sedláček, On a set system, Annals New York Acad. Sci., 175 (No. 1, 1970), 329-330.

Index entries for linear recurrences with constant coefficients, signature (0,1).

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

Cf. A002848, A002849, A108235.

Sequence in context: A344323 A368826 A352150 * A097887 A019761 A188614

Adjacent sequences: A161823 A161824 A161825 * A161827 A161828 A161829

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 10 2010

Status

approved