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The Fibonacci sequence, $F_n = F_{n - 1} + F_{n - 2}$, and its counterpartfor $n < 0$, the negaFibonacci sequence, $F_{-n} = (-1)^{n + 1} \cdot F_n$, areamong the most studied sequences in mathematics. In this paper we will presenta new kind of sequence, the negaFibonacci-esque sequences, identified by theproperty that $\omega_n = \omega_{n - 2} - \omega_{n - 1}$ with $\omega_1,\omega_2 \in \mathbb{C}$ chosen at will. We will partition this kind intonatural complete and complex complete negaFibonacci-esque sequences.We willprove that $\frac{1}{\phi^n}$, referred to as the principal negaFibonacci-esquesequence, is not only a complex complete negaFibonacci-esque sequence but alsoone of the most significant. Furthermore, we will present an explicit formulafor all complex complete negaFibonacci-esque sequences constructed with acombination of two negaFibonacci terms. We shall then conclude by connectingthese sequences to the golden spiral and ratio.

On negaFibonacci-esque Sequences and Their Relation to the Golden Ratio