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x

 母函数加排除法

 你们真的觉得论坛里爬楼梯的题目不够多吗 逢8必蹬，于是中间段是\$x^n\$，前后段生成函数计算，相乘。

 真的觉得论坛里爬楼梯的题目不够多吗

 倪举鹏 发表于 2019-4-12 11:56 母函数加排除法 期待大佬写程序

楼主| 发表于 2019-4-13 06:40:23 | 显示全部楼层
 本帖最后由 王守恩 于 2019-4-13 06:41 编辑 markfang2050 发表于 2019-4-12 18:51 期待大佬写程序 谢谢 zeroieme ！   逢\(\ \ 8\ \ \)必蹬！于是中间段是\(\ \ x^n\)，前后段生成函数计算，相乘。 前段：第 1 级到第 8 级有 3 种蹬法， 中间段：分2节，8——18——28，每节有 5 种蹬法， 后段：第 28 级到第 35 级有 3 种蹬法， 合计：3×5^2×3=225 种蹬法。

 程序计算得 ------------------- 225

 {{2, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {2, 5, 8, 10,   12, 15, 18, 20, 22, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 12, 15, 18,   20, 22, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 20, 23, 25,   28, 30, 32, 35}, {2, 5, 8, 10, 12, 15, 18, 20, 23, 25, 28, 30, 33,   35}, {2, 5, 8, 10, 12, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {2, 5,   8, 10, 12, 15, 18, 20, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 12,   15, 18, 20, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 20,   23, 26, 28, 31, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 21, 23, 25, 28,   30, 32, 35}, {2, 5, 8, 10, 12, 15, 18, 21, 23, 25, 28, 30, 33,   35}, {2, 5, 8, 10, 12, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {2, 5,   8, 10, 12, 15, 18, 21, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 12,   15, 18, 21, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 12, 15, 18, 21,   23, 26, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 22, 25, 28,   30, 32, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 22, 25, 28, 30, 33,   35}, {2, 5, 8, 10, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {2, 5,   8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 10, 13,   15, 18, 20, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 20,   23, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28,   30, 32, 35}, {2, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28, 30, 33,   35}, {2, 5, 8, 10, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {2, 5,   8, 10, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 10, 13,   15, 18, 21, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 21,   23, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 15, 18, 21, 23, 26, 28,   30, 32, 35}, {2, 5, 8, 10, 13, 15, 18, 21, 23, 26, 28, 30, 33,   35}, {2, 5, 8, 10, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {2, 5,   8, 10, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {2, 5, 8, 10, 13,   16, 18, 20, 22, 25, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 20,   22, 25, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 20, 23, 25, 28,   30, 32, 35}, {2, 5, 8, 10, 13, 16, 18, 20, 23, 25, 28, 30, 33,   35}, {2, 5, 8, 10, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {2, 5,   8, 10, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 13,   16, 18, 20, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 20,   23, 26, 28, 31, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 21, 23, 25, 28,   30, 32, 35}, {2, 5, 8, 10, 13, 16, 18, 21, 23, 25, 28, 30, 33,   35}, {2, 5, 8, 10, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {2, 5,   8, 10, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 10, 13,   16, 18, 21, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 10, 13, 16, 18, 21,   23, 26, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 22, 25, 28,   30, 32, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 22, 25, 28, 30, 33,   35}, {2, 5, 8, 11, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {2, 5,   8, 11, 13, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 11, 13,   15, 18, 20, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 20,   23, 25, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 23, 26, 28,   30, 32, 35}, {2, 5, 8, 11, 13, 15, 18, 20, 23, 26, 28, 30, 33,   35}, {2, 5, 8, 11, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {2, 5,   8, 11, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {2, 5, 8, 11, 13,   15, 18, 21, 23, 25, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 21,   23, 25, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 15, 18, 21, 23, 26, 28,   30, 32, 35}, {2, 5, 8, 11, 13, 15, 18, 21, 23, 26, 28, 30, 33,   35}, {2, 5, 8, 11, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {2, 5,   8, 11, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {2, 5, 8, 11, 13,   16, 18, 20, 22, 25, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 20,   22, 25, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 20, 23, 25, 28,   30, 32, 35}, {2, 5, 8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 33,   35}, {2, 5, 8, 11, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {2, 5,   8, 11, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 11, 13,   16, 18, 20, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 20,   23, 26, 28, 31, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 21, 23, 25, 28,   30, 32, 35}, {2, 5, 8, 11, 13, 16, 18, 21, 23, 25, 28, 30, 33,   35}, {2, 5, 8, 11, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {2, 5,   8, 11, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {2, 5, 8, 11, 13,   16, 18, 21, 23, 26, 28, 30, 33, 35}, {2, 5, 8, 11, 13, 16, 18, 21,   23, 26, 28, 31, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28,   30, 32, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 30, 33,   35}, {3, 5, 8, 10, 12, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 5,   8, 10, 12, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 12,   15, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 20,   23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 23, 26, 28,   30, 32, 35}, {3, 5, 8, 10, 12, 15, 18, 20, 23, 26, 28, 30, 33,   35}, {3, 5, 8, 10, 12, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 5,   8, 10, 12, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 12,   15, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 21,   23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 12, 15, 18, 21, 23, 26, 28,   30, 32, 35}, {3, 5, 8, 10, 12, 15, 18, 21, 23, 26, 28, 30, 33,   35}, {3, 5, 8, 10, 12, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 5,   8, 10, 13, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 13,   15, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 20,   22, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28,   30, 32, 35}, {3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 33,   35}, {3, 5, 8, 10, 13, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 5,   8, 10, 13, 15, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 5, 8, 10, 13,   15, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 20,   23, 26, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 21, 23, 25, 28,   30, 32, 35}, {3, 5, 8, 10, 13, 15, 18, 21, 23, 25, 28, 30, 33,   35}, {3, 5, 8, 10, 13, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 5,   8, 10, 13, 15, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 5, 8, 10, 13,   15, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 15, 18, 21,   23, 26, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 22, 25, 28,   30, 32, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 22, 25, 28, 30, 33,   35}, {3, 5, 8, 10, 13, 16, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 5,   8, 10, 13, 16, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 13,   16, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 20,   23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 23, 26, 28,   30, 32, 35}, {3, 5, 8, 10, 13, 16, 18, 20, 23, 26, 28, 30, 33,   35}, {3, 5, 8, 10, 13, 16, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 5,   8, 10, 13, 16, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 10, 13,   16, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 21,   23, 25, 28, 31, 33, 35}, {3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 28,   30, 32, 35}, {3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 28, 30, 33,   35}, {3, 5, 8, 10, 13, 16, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 5,   8, 11, 13, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 5, 8, 11, 13,   15, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 20,   22, 25, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 20, 23, 25, 28,   30, 32, 35}, {3, 5, 8, 11, 13, 15, 18, 20, 23, 25, 28, 30, 33,   35}, {3, 5, 8, 11, 13, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 5,   8, 11, 13, 15, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 5, 8, 11, 13,   15, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 20,   23, 26, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 21, 23, 25, 28,   30, 32, 35}, {3, 5, 8, 11, 13, 15, 18, 21, 23, 25, 28, 30, 33,   35}, {3, 5, 8, 11, 13, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 5,   8, 11, 13, 15, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 5, 8, 11, 13,   15, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 15, 18, 21,   23, 26, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 22, 25, 28,   30, 32, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 22, 25, 28, 30, 33,   35}, {3, 5, 8, 11, 13, 16, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 5,   8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 11, 13,   16, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 20,   23, 25, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 23, 26, 28,   30, 32, 35}, {3, 5, 8, 11, 13, 16, 18, 20, 23, 26, 28, 30, 33,   35}, {3, 5, 8, 11, 13, 16, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 5,   8, 11, 13, 16, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 5, 8, 11, 13,   16, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 21,   23, 25, 28, 31, 33, 35}, {3, 5, 8, 11, 13, 16, 18, 21, 23, 26, 28,   30, 32, 35}, {3, 5, 8, 11, 13, 16, 18, 21, 23, 26, 28, 30, 33,   35}, {3, 5, 8, 11, 13, 16, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 6,   8, 10, 12, 15, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 6, 8, 10, 12,   15, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 20,   22, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 20, 23, 25, 28,   30, 32, 35}, {3, 6, 8, 10, 12, 15, 18, 20, 23, 25, 28, 30, 33,   35}, {3, 6, 8, 10, 12, 15, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 6,   8, 10, 12, 15, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 10, 12,   15, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 20,   23, 26, 28, 31, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 21, 23, 25, 28,   30, 32, 35}, {3, 6, 8, 10, 12, 15, 18, 21, 23, 25, 28, 30, 33,   35}, {3, 6, 8, 10, 12, 15, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 6,   8, 10, 12, 15, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 10, 12,   15, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 12, 15, 18, 21,   23, 26, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 22, 25, 28,   30, 32, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 22, 25, 28, 30, 33,   35}, {3, 6, 8, 10, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 6,   8, 10, 13, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 6, 8, 10, 13,   15, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 20,   23, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 23, 26, 28,   30, 32, 35}, {3, 6, 8, 10, 13, 15, 18, 20, 23, 26, 28, 30, 33,   35}, {3, 6, 8, 10, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 6,   8, 10, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 6, 8, 10, 13,   15, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 21,   23, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 15, 18, 21, 23, 26, 28,   30, 32, 35}, {3, 6, 8, 10, 13, 15, 18, 21, 23, 26, 28, 30, 33,   35}, {3, 6, 8, 10, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 6,   8, 10, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 6, 8, 10, 13,   16, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 20,   22, 25, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 20, 23, 25, 28,   30, 32, 35}, {3, 6, 8, 10, 13, 16, 18, 20, 23, 25, 28, 30, 33,   35}, {3, 6, 8, 10, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 6,   8, 10, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 10, 13,   16, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 20,   23, 26, 28, 31, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 21, 23, 25, 28,   30, 32, 35}, {3, 6, 8, 10, 13, 16, 18, 21, 23, 25, 28, 30, 33,   35}, {3, 6, 8, 10, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 6,   8, 10, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 10, 13,   16, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 10, 13, 16, 18, 21,   23, 26, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 22, 25, 28,   30, 32, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 22, 25, 28, 30, 33,   35}, {3, 6, 8, 11, 13, 15, 18, 20, 22, 25, 28, 31, 33, 35}, {3, 6,   8, 11, 13, 15, 18, 20, 23, 25, 28, 30, 32, 35}, {3, 6, 8, 11, 13,   15, 18, 20, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 20,   23, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 23, 26, 28,   30, 32, 35}, {3, 6, 8, 11, 13, 15, 18, 20, 23, 26, 28, 30, 33,   35}, {3, 6, 8, 11, 13, 15, 18, 20, 23, 26, 28, 31, 33, 35}, {3, 6,   8, 11, 13, 15, 18, 21, 23, 25, 28, 30, 32, 35}, {3, 6, 8, 11, 13,   15, 18, 21, 23, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 21,   23, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28,   30, 32, 35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28, 30, 33,   35}, {3, 6, 8, 11, 13, 15, 18, 21, 23, 26, 28, 31, 33, 35}, {3, 6,   8, 11, 13, 16, 18, 20, 22, 25, 28, 30, 32, 35}, {3, 6, 8, 11, 13,   16, 18, 20, 22, 25, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20,   22, 25, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28,   30, 32, 35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 33,   35}, {3, 6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 31, 33, 35}, {3, 6,   8, 11, 13, 16, 18, 20, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 11, 13,   16, 18, 20, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 20,   23, 26, 28, 31, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28,   30, 32, 35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28, 30, 33,   35}, {3, 6, 8, 11, 13, 16, 18, 21, 23, 25, 28, 31, 33, 35}, {3, 6,   8, 11, 13, 16, 18, 21, 23, 26, 28, 30, 32, 35}, {3, 6, 8, 11, 13,   16, 18, 21, 23, 26, 28, 30, 33, 35}, {3, 6, 8, 11, 13, 16, 18, 21,   23, 26, 28, 31, 33, 35}} 225种登高方案。@守恩王

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GMT+8, 2019-12-12 06:27 , Processed in 0.061571 second(s), 17 queries .