Abstract
This paper investigated how many different ways an $m$-rung staircase can be climbed within certain rules. It was observed that the climbing numbers of the stairs are related to the Catalan numbers. The combinatorics problem discussed in this article is different from the ones done so far and is related not only to Catalan numbers but also to some Fuss-Catalan numbers. Some results regarding the climbing numbers were obtained. It was observed that with the initial ascent being fixed, the climbing numbers of stairs with $m, m+1, m+2, m+3$, ... rungs, where $m>1$ is an integer, are related to respectively some Fuss-Catalan numbers.
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