🔁 线性递推计算器Linear Recurrence Calculator
计算常系数线性递推：给定初值与系数 a_n = c1 a_{n-1}+…。本地处理。可设置「项数」、「初值（空格分隔）」、「系数 c1 c2 …（对应 a_{n-1}, a_{n-2}, …）」。Compute a linear recurrence with constant coefficients from seeds and coeffs. Processed locally. Settings: Terms, Seeds (spaces), Coeffs c1 c2 … (for a_n-1, a_n-2, …).
使用说明与常见问题How-to & FAQ
「线性递推计算器」是什么？What is the Linear Recurrence Calculator tool?
计算常系数线性递推：给定初值与系数 a_n = c1 a_{n-1}+…。本地处理。可设置「项数」、「初值（空格分隔）」、「系数 c1 c2 …（对应 a_{n-1}, a_{n-2}, …）」。Compute a linear recurrence with constant coefficients from seeds and coeffs. Processed locally. Settings: Terms, Seeds (spaces), Coeffs c1 c2 … (for a_n-1, a_n-2, …).
如何使用「线性递推计算器」？How do I use the Linear Recurrence Calculator tool?
在「线性递推计算器」中，按需设置「项数」、「初值（空格分隔）」、「系数 c1 c2 …（对应 a_{n-1}, a_{n-2}, …）」，结果会实时显示在下方，点击「复制结果」即可复制。In the Linear Recurrence Calculator: Adjust "Terms", "Seeds (spaces)", "Coeffs c1 c2 … (for a_n-1, a_n-2, …)"; the result appears below instantly — click "Copy result" to copy it.
怎么得到斐波那契数列？How do I get the Fibonacci numbers?
初值填 0 1，系数填 1 1，即 aₙ = 1·aₙ₋₁ + 1·aₙ₋₂。改成初值 2 1 就是卢卡斯数列，系数 2 1 是佩尔数列一类的递推。Enter seeds 0 1 and coefficients 1 1, meaning aₙ = 1·aₙ₋₁ + 1·aₙ₋₂. Seeds 2 1 give the Lucas numbers, and coefficients 2 1 give a Pell-type recurrence.
输入和输出是什么样的？What does the input and output look like?
例如在「线性递推计算器」中把「项数」设为 6，「初值（空格分隔）」设为 0 1，「系数 c1 c2 …（对应 a_{n-1}, a_{n-2}, …）」设为 1 1，输出为：0 ⏎ 1 ⏎ 1 ⏎ 2 ⏎ 3 ⏎ 5（⏎ 表示换行）。For example, in the Linear Recurrence Calculator with "Terms" set to 6, "Seeds (spaces)" set to 0 1, "Coeffs c1 c2 … (for a_n-1, a_n-2, …)" set to 1 1, the output is: 0 ⏎ 1 ⏎ 1 ⏎ 2 ⏎ 3 ⏎ 5 (⏎ marks a line break).
有哪些选项可以调整？What options can I adjust?
「线性递推计算器」的设置：「项数」默认 15；「初值（空格分隔）」默认 0 1；「系数 c1 c2 …（对应 a_{n-1}, a_{n-2}, …）」默认 1 1。每次生成结果都按当前设置处理。Settings in the Linear Recurrence Calculator — "Terms" default 15; "Seeds (spaces)" default 0 1; "Coeffs c1 c2 … (for a_n-1, a_n-2, …)" default 1 1. The result always uses the current settings.
计算精度如何？How precise are the results?
「线性递推计算器」中的整数都用大整数（BigInt）精确计算，不经过浮点，所以再长的项也不会丢失位数；输入超出页面说明的范围时会给出提示，而不是悄悄截断。Integers in the Linear Recurrence Calculator are computed exactly with big integers (BigInt), with no floating-point step, so even very long terms keep every digit; values outside the stated ranges give a message instead of being silently cut off.
「线性递推计算器」免费吗？需要注册吗？Is the Linear Recurrence Calculator free? Do I need an account?
「线性递推计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Linear Recurrence Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.