In this study, mainly we deal with a Banach space-value Motzkin sequence spaces. First, we constructed the sequence spaces \(\ell _{\infty }\left( \mathcal {M},V\right) ,\) \(c_{0}\left( \mathcal {M},V\right)\) and \(\ell _{p}\left( \mathcal {M},V\right)\) for \(1\le p<\infty\) , formed by a special Banach space V. Here, \(\mathcal {M}\) represents the Motzkin matrix constructed using the Motzkin numbers known in the literature. Then, we defined a new type of Schauder basis for \(c_{0}\left( \mathcal {M},V\right)\) and \(\ell _{p}\left( \mathcal {M},V\right)\) . We attempted to provide a simple method that simulates the reduction of the total energies of certain signal groups via the norm in the Motzkin sequence space \(c_{0}\left( \mathcal {M},L_{2}\left[ -\pi ,\pi \right] \right)\) . Furthermore, some properties of Motzkin sequence space, such as Radon-Riesz, Dunford -Pettis, Approximation properties are examined. Dunford-Pettis property (DPP) facilitates the prediction of operator behavior on a space; specifically, if a space possesses the DPP, the distinction between weakly compact operators and completely continuous operators disappears. Consequently, this simplifies the spectral theoretical analysis of certain classes, such as integral and kernel operators. Based on our main result in the work, we conclude that the Motzkin sequence space \(\ell _{1}\left( \mathcal {M},V\right)\) also enjoys these specific advantages. While establishing weak convergence is often simpler in functional analysis, proving strong convergence is typically more challenging. The Radon-Riesz property allows for a direct transition from the convergence of the scalar sequence \(\left( \left\| u_{n}\right\| \right)\) to the convergence of the sequence \(\left( u_{n}\right)\) in the norm topology of X. We proved finally that the Motzkin sequence space \(\ell _{2}\left( \mathcal {M},V\right)\) also possesses this advantage.
