Basic sequences

[Lucaswaters3]

(A2- a1) x3=
3, 17, 59, 126, 201, 225 ,72, -459, -1593
126 is divisible by 3,6, and 9
Is this a new sequence, I couldn't find anything about it online? It seems important, I wanted to share it!

 

[Romsek]

 

[Dr.Peterson]

(A2- a1) x3=
3, 17, 59, 126, 201, 225 ,72, -459, -1593
126 is divisible by 3,6, and 9
Is this a new sequence, I couldn't find anything about it online? It seems important, I wanted to share it!

You'll have to use words to explain what you are thinking.

It looks as if you are saying that you add 3 times the difference of the first two terms, to get the third; that is, [MATH]a_3 = a_2 + 3(a_2 - a_1)[/MATH]. That yields your third term: [MATH]a_3 = 17 + 3(17 - 3) = 17 + 42 = 59[/MATH].

But if I repeat the same thing, [MATH]a_{n+1} = a_n + 3(a_n - a_{n-1})[/MATH], I don't get the 4th term: [MATH]a_4 = a_3 + 3(a_3 - a_2) = 59 + 3(59 - 17) = 59 + 126 = 185[/MATH]. At this point, it looks like you're doing [MATH]a_{n+1} = 3(a_n - a_{n-1})[/MATH]. But that's not how you got the third term.

So, please tell us exactly what you're doing, in words.

And then, explain why you think it's important.

In any case, this doesn't belong in the News forum.