数学吧应该多一些开放性问题
a(n)是从1开始,通过交替加乘达到n的方法数,其中每次运算对象在集合A中(如A={2,3},n=12,(1+2)*3+3=12为一种方法)
可以根据最后一次运算为加法还是乘法分拆成两个数列再进行递推
有图像看出A中元素尽量互素时数列值的范围更集中
当A中不含2时,由于n=2时会出现0的“异常值”,在后续递推时造成的影响会逐步放大,造成图像“波动上升”的现象
当A满足某种条件时,a(n)/n趋向于0
下图分别为23,234,235,236,237,238,345,456
欢迎讨论,对于这种问题有没有合适的分析方法
![](http://tiebapic.baidu.com/forum/w%3D580/sign=8cf9ed0f6e381f309e198da199004c67/012f6709c93d70cf2911753abedcd100baa12b2b.jpg?tbpicau=2024-07-02-05_5e0710d2789b1cb2d6108589028a9163)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=beca6d06e78b87d65042ab1737092860/5b0e95cad1c8a786c4c195392109c93d70cf502b.jpg?tbpicau=2024-07-02-05_ec4b4470f9e128045cd76114b703a8f7)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=36a9742841082838680ddc1c8898a964/b7067f3e6709c93d6119d1c0d93df8dcd100542b.jpg?tbpicau=2024-07-02-05_bd11480896ff4671824dcda8c416b03c)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=b1d7a60f28061d957d4637304bf50a5d/86cdd100baa1cd116a5dad17ff12c8fcc3ce2d2b.jpg?tbpicau=2024-07-02-05_cc5e866e25dad7670721dbf60de5d77b)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=55de84015b950a7b75354ecc3ad0625c/af11baa1cd11728b5ec653158efcc3cec3fd2c2b.jpg?tbpicau=2024-07-02-05_d0a3141d2401dc41430a81d73998a56b)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=16ade80f3df40ad115e4c7eb672d1151/0c9a4710b912c8fcdf1829faba039245d688212b.jpg?tbpicau=2024-07-02-05_96b8ba1b3d9c02250ad993cc40424b90)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=8d3a6014252762d0803ea4b790ed0849/a899d43f8794a4c259c8381c48f41bd5ad6e392b.jpg?tbpicau=2024-07-02-05_be261c80db6be2ebc80b01879152dda4)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=320943ebcc13632715edc23ba18ea056/ec54d688d43f879487149719941b0ef41bd53a2b.jpg?tbpicau=2024-07-02-05_d758fcccb778b959944a6feefa7f7e25)
a(n)是从1开始,通过交替加乘达到n的方法数,其中每次运算对象在集合A中(如A={2,3},n=12,(1+2)*3+3=12为一种方法)
可以根据最后一次运算为加法还是乘法分拆成两个数列再进行递推
有图像看出A中元素尽量互素时数列值的范围更集中
当A中不含2时,由于n=2时会出现0的“异常值”,在后续递推时造成的影响会逐步放大,造成图像“波动上升”的现象
当A满足某种条件时,a(n)/n趋向于0
下图分别为23,234,235,236,237,238,345,456
欢迎讨论,对于这种问题有没有合适的分析方法
![](http://tiebapic.baidu.com/forum/w%3D580/sign=8cf9ed0f6e381f309e198da199004c67/012f6709c93d70cf2911753abedcd100baa12b2b.jpg?tbpicau=2024-07-02-05_5e0710d2789b1cb2d6108589028a9163)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=beca6d06e78b87d65042ab1737092860/5b0e95cad1c8a786c4c195392109c93d70cf502b.jpg?tbpicau=2024-07-02-05_ec4b4470f9e128045cd76114b703a8f7)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=36a9742841082838680ddc1c8898a964/b7067f3e6709c93d6119d1c0d93df8dcd100542b.jpg?tbpicau=2024-07-02-05_bd11480896ff4671824dcda8c416b03c)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=b1d7a60f28061d957d4637304bf50a5d/86cdd100baa1cd116a5dad17ff12c8fcc3ce2d2b.jpg?tbpicau=2024-07-02-05_cc5e866e25dad7670721dbf60de5d77b)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=55de84015b950a7b75354ecc3ad0625c/af11baa1cd11728b5ec653158efcc3cec3fd2c2b.jpg?tbpicau=2024-07-02-05_d0a3141d2401dc41430a81d73998a56b)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=16ade80f3df40ad115e4c7eb672d1151/0c9a4710b912c8fcdf1829faba039245d688212b.jpg?tbpicau=2024-07-02-05_96b8ba1b3d9c02250ad993cc40424b90)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=8d3a6014252762d0803ea4b790ed0849/a899d43f8794a4c259c8381c48f41bd5ad6e392b.jpg?tbpicau=2024-07-02-05_be261c80db6be2ebc80b01879152dda4)
![](http://tiebapic.baidu.com/forum/w%3D580/sign=320943ebcc13632715edc23ba18ea056/ec54d688d43f879487149719941b0ef41bd53a2b.jpg?tbpicau=2024-07-02-05_d758fcccb778b959944a6feefa7f7e25)