On the norm of circulant matrices containing 4th order recurrence relations

In this study, the sum of first 𝑛 terms of this series is formulated by obtaining the Binet formula for the generalized Tetranacci sequence (𝒯𝑛)𝑛∈ℕ, whose initial values are 𝒯0 = 𝑎,𝒯1 = 𝑏,𝒯2 = 𝑐, 𝒯3 = 𝑑 and defined by the 𝒯𝑛 = 𝑝𝒯𝑛−1 + 𝑞𝒯𝑛−2 + 𝑟𝒯𝑛−3 + 𝑠𝒯𝑛−4 recurrence relation for 𝑛 ≥ 4. The generating function was obtained for generalized Tetranacci number sequence. In addition, some matrix norms were calculated for the circulant matrices consisting of elements of the generalized Tetranacci number sequence.