Sum-distinct sequences and Fibonacci numbers (Q914722)

Positive integers \(a_ 1<a_ 2<...<a_ n\) are called a sum-distinct sequence if all the \(2^ n\) subsums are distinct. Two sequences \(A=\{a_ 1,a_ 2,...\}\) and \(B=\{b_ 1,b_ 2,...\}\) are said to be compatible sum-distinct sequences, if both A and B are sum-distinct and the subsums of A differ from those of B. By using Fibonacci numbers special compatible sum-distinct sequences are constructed. The same is done by using generalized Fibonacci numbers, defined by \(F_ t(n)=n\), \(n=1,...,t\), \(F_ t(n+1)=F_ t(n)+F_ t(n-t+1),\quad n\geq t;\) t a fixed natural number.