# Thread: General Term of Set of Data

1. ## General Term of Set of Data

Can anyone give me the general term, t_n, or pattern for the following data:
...0, 1, 4, 5, 8, 9, 12, 13, 16, 17...
including negatives.

2. Originally Posted by blaise
Can anyone give me the general term, t_n, or pattern for the following data:
...0, 1, 4, 5, 8, 9, 12, 13, 16, 17...
including negatives.
$a_n=a_{n-2}+4$

with $a_0=0,\ a_1=1$

.

3. Ah, I was hoping it wouldn't be recursive.
Thanks a lot, though.

4. Originally Posted by blaise
Ah, I was hoping it wouldn't be recursive.
Thanks a lot, though.
Non-recursive you say:

$a_{n}=4\times \lfloor n/2\rfloor +(n-2\times \lfloor n/2\rfloor)=2\times \lfloor n/2\rfloor +n$

.

5. Originally Posted by blaise
Can anyone give me the general term, t_n, or pattern for the following data:
...0, 1, 4, 5, 8, 9, 12, 13, 16, 17...
including negatives.
$t_{2n+1} = 4n$ and $t_{2n+2} = 4n + 1$.