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Math Help - General Term of Set of Data

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by blaise View Post
    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

    .
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  3. #3
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    Ah, I was hoping it wouldn't be recursive.
    Thanks a lot, though.
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  4. #4
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    Quote Originally Posted by blaise View Post
    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

    .
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  5. #5
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    Quote Originally Posted by blaise View Post
    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.
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