Fibr\'e vectoriel de rang $2n+1$ sur l'espace $\mathbb{P}^{2n+2}$

We build in this article new families of algebraic vector bundles of rank $2n+1$ on the complex projective space $\mathbb{P}^{2n +2}$ from two bundles of rank $2n$ on $\mathbb{P}^{2n+1}$, the weighted null correlation bundles \cite{bah2} and the weighted Tango bundles \cite{bah1} while using the method of Kumar-Peterson-Rao \cite{ku-ra-pe}. We construct another example of vector bundle of rank 3 on $\mathbb{P}_\mathbb{K}^4$ different than the one presented in \cite{ku-ra-pe}, where $\mathbb{K}$ is any field.