General Term of Set of Data

**blaise** · December 29th 2008, 10:43 PM

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.

**Constatine11** · December 29th 2008, 11:03 PM

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 $a_0=0,\ a_1=1$

.

**blaise** · December 29th 2008, 11:18 PM

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

**Constatine11** · December 30th 2008, 01:34 AM

Originally Posted by blaise

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

Non-recursive you say:

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

.

**mr fantastic** · December 30th 2008, 01:52 AM

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 $t_{2n+2} = 4n + 1$ .

Thread: General Term of Set of Data