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In the first part of this paper I give an elementary overview about somenumber sequences which count various sorts of lattice paths in strips along thex-axis and compute their generating functions in terms of Fibonacci and Lucaspolynomials. In the second part I generalize these results by introducingsuitable weights and study some special cases in more detail. In the course ofthis work I have been led to curious number triangles and various conjectures

Some remarks and conjectures related to lattice paths in strips along the x-axis