We give a generalization of $k$-bonacci numbers where $k$ is a positive rational number. These numbers enumerate binary words of size $n$ whose maximal factors of the form $0^a1^b$ satisfy $ak > b$ or $a = 0$.

翻译：以美元为正合理数字,我们给出了k美元-bonacci数字的概略法,其中K美元是一个正合理数字。这些数字列举了以美元为单位的二进制字数,其最大因子为$0+a1b$满足了$ > b$或$a=0美元。