The Linear Wireless Sensor Networks (LWSN) are a collection of wireless sensors arranged in a linear fashion. In order to allow them a better organization, several topologies have been proposed in the research. One of the most recent of them assumes a topology called redundant k-variant in which the redundancy factor k is a variable. This topology is based on a model generating the Euclidean positions of the nodes in an increasing way, the topology divides the network into two groups of nodes with different redundancy factors. This topology model increases the availability of the network especially in the areas close to the sink, compared to other topological models in which the redundancy factor was fixed for all the nodes of the network.In this paper we propose a generalization of the mathematical model proposed in the redundant k-variant model by generalizing the variation of the redundancy factor for all the nodes of the network and thus eliminating the fixed nature of the redundancy factor within the groups of nodes in the network in the k-variant model.In the approach proposed in this paper, the redundancy factor varies as one moves away from the sink. In this model, we choose, for each node, the best position among all possible ones. We use a system based on an arithmetic sequence to define an equation whose solution will generate the positions of the different nodes. We have also defined a specific resolution method coded in Python to choose the right values from all the solutions.The simulations focused on four series of transmissions based on different topologies. The experiments showed a much higher energy efficiency of the network in favor of the proposed model.