On Propagation Sequence

A sequence is a function whose domain is the set of natural numbers (or sometimes ) and whose codomain is a given set . Formally, a sequence in is a function: where denotes the th term of the sequence. Fibonacci sequence is known in mathematics as the sequence in which each term after its first two terms is the sum of two preceding terms. The importance of the sequence is underpinned by its appeal from nature, and thus to scientists who are interested in the development and growth patterns in nature. In this seminal paper, we announce a new sequence called propagation or polygon sequence, of which Fibonacci sequence is only a subsequence, and investigate its golden ratio and properties. Population studies require the development of appropriate models for determining growth trends. In this communication, we have characterized and established a mathematical relationship between two principal subsequences of the propagation sequence (one of the subsequences being Fibonacci sequence), which yields an integral factor. We establish bounds of the integral factor within suitable ranges. Furthermore, we derive a propagation population model and propagation differential equation, both of which suggest potential for future research interests and engagement. This relates to propagation sequence because of the inherent generative nature in population growth of species of interest.