The Fibonacci Octonions

Horadam Octonions

“…In the next section we define a new octonion sequence with Horadam components which is generalization of earlier studies, for example, see [3,11,12,17,21,22,23]. And then we give some fundamental properties and identities related with this sequences.…”

“…We should note that the equation (3.6) is Binet formula of Modified Pell octonions which is given by Catarino in [3]. Also, if we take A = B = 1, and calculate the value α, β with respect to its recurrence relation, we have Binet formula for Fibonacci octonions which is given by Keçilioglu and Akkuş in [17].…”

“…More recently octonions have been studied by many authors. For example, the Fibonacci octonions, Pell octonions and Modified Pell octonions appeared in [3,17,22]. There are many studies about Fibonacci numbers over dual octonions and generalized octonions [11,21,23].…”

“…Cassini identities are studied for Fibonacci octonions in [12,17] and for Modified Pell octonions in [3].…”

The Third Order Jacobsthal Octonions: Some Combinatorial Properties

“…This approach was originally proposed by Horadam and Iyer in the articles [13,16] for Fibonacci quaternions. The methods used by Horadam and Iyer in that papers have been recently applied to the other familiar octonion numbers by several authors [1,5,10,18]. This paper has three main sections.…”