This paper examines the Fibonacci quaternion sequence
with quadruple-produce components, and demonstrates a golden-like ra-
tio and some identities for this sequence. Its generating and exponential
generating functions are given. Along with these, its series and binomial
sum formula are established.
In this article, we construct the plastic number in the three-dimensional
space. We examine the nested radicals and continued fraction expansions of the plastic ratio.
In addition, we give some properties and geometric interpretations of the plastic constant.