MathDB

Find all triples

(a,b,c)

of real numbers for which there exists a function

f:\mathbb{Z}^{+}\rightarrow\mathbb{Z}^{+}

satisfying

af(n)+bf(n+1)+cf(n+2)<0

for every

n\in\mathbb{Z}^{+}

(

\mathbb{Z}^{+}

denotes the set of positive integers).
Proposed by András Imolay, Budapest

Problem Statement