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Thread: Interesting sequence - find closed form

  1. #1
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    Interesting sequence - find closed form

    This sequence has me stumped.... anyone have an idea on what the closed form is?

    0, 1, 4, 12, 28, 55, 96, 154
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by vexiked View Post
    This sequence has me stumped.... anyone have an idea on what the closed form is?

    0, 1, 4, 12, 28, 55, 96, 154
    I'm not surprised, see this

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    I'm not surprised, see this

    CB
    Whoa! awesome resource. CaptainBlack, can you point me to a sticky with useful links such as that? I've been searching around with the google, but come up with too much random junk.

    Thanks!
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  4. #4
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    Quote Originally Posted by vexiked View Post
    This sequence has me stumped.... anyone have an idea on what the closed form is?

    0, 1, 4, 12, 28, 55, 96, 154
    Labelling $\displaystyle a_0, a_1, a_2, \ldots$ . Then $\displaystyle a_1$ is the first triangular number, $\displaystyle a_2$ is the second square number, $\displaystyle a_3$ is the third pentagonal number, etc...

    I'm just working on a closed form but it shouldn't be too difficult at all.

    Pomp

    EDIT: $\displaystyle a_n = n \left( {}^nC_2 + 1 \right)$ works.
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