英文:
How to find sequence formula
问题
我正在寻找一个序列的公式。这个序列是{1,5,18, 56,160,432}。
我尝试使用Wolfram的Mathematica - FindSequenceFunction和FindGeneratingFunction。第一个没有给我一个函数，第二个给了我1-n/(1-2n)^3，我不确定这是否正确。也许我没有正确理解Mathematica。谢谢帮助。
英文:
I am looking for a sequence formula. The sequence is {1,5,18, 56,160,432}.
I tried using wolframs mathematica - FindSequenceFunction and FindGeneratingFunction. First one did not even give me a function, second one gave me 1-n/(1-2n)^3 which i dont see how this can be right. Maybe I dont understand mathematica properly. Thanks for help
答案1
得分: 0
前往 https://oeis.org/，输入 1,5,18,56,160,432，然后点击搜索。在一瞬间，它会找到你不是第一个查看该序列的人，实际上，该序列已经在两种不同的上下文中出现过。
英文:
Go to
https://oeis.org/
and enter
1,5,18,56,160,432
and tap Search
and in a fraction of a second it finds that you are not the first person looking at that sequence, that sequence has actually shown up in two different contexts.
答案2
得分: 0
fn[x_] := Evaluate[FindGeneratingFunction[{1, 5, 18, 56, 160, 432}, x]]
Series[fn[x], {x, 0, 5}]
1 + 5 x + 18 x^2 + 56 x^3 + 160 x^4 + 432 x^5 + O[x]^6
FindSequenceFunction needs another couple of terms before it nails it
FindSequenceFunction[{1, 5, 18, 56, 160, 432, 1120, 2816}, n]
2^(-3 + n) n (3 + n)
Same as OEIS A001793
英文:
fn[x_] := Evaluate[
FindGeneratingFunction[{1, 5, 18, 56, 160, 432}, x]]
Series[fn[x], {x, 0, 5}]
> 1 + 5 x + 18 x^2 + 56 x^3 + 160 x^4 + 432 x^5 + O[x]^6
FindSequenceFunction needs another couple of terms before it nails it
FindSequenceFunction[{1, 5, 18, 56, 160, 432, 1120, 2816}, n]
> 2^(-3 + n) n (3 + n)
Same as OEIS A001793
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