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前段时间,笔者遇到了这样一道习题:一个含有10项的数列an满足:a1=0,a10=5,ak+1-ak=1,(k=1,2,…,9),则符合这样条件的数列an有____个。在解答本题的过程中,笔者经过反复尝试,最后把问题情境转化为:设一个机器小人初始位置在下图的网格A(1,0)处,每一次移动由两部分构成:向右移动一个单位,同时向上(或向下)移动一个单位(符合ak+1-ak=1),这样经过9次移动后到达点B(10,5)。
Some time ago, I encountered such a problem: a sequence containing an 10 an satisfy: a1 = 0, a10 = 5, ak + 1-ak = 1, (k = 1,2, ..., 9), then in line with this The sequence of conditions an has ____. In the process of answering this question, after repeated attempts, the author finally translates the problem situation into: Setting a Machine The villain initial position is in the grid A (1,0) below. Each movement consists of two parts: moving to the right A unit moves up (or down) by one unit (ak + 1-ak = 1) at the same time so that it reaches point B (10,5) after 9 moves.