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    Here's a slightly unusual Stats problem. It's basically an issue of counting. Explaining would be hopeless (this isn't an exam question or problem, it's a real life application though only important for accountancy really) so I will try and demonstrate:

    If n=3: Count is Ma3, Ma2b, Mabc -> c=3
    If n=4: Count is Ma4, Ma3b, Ma2bc, Ma2b2, Mabcd -> c=5
    If n=5: Count is Ma5, Ma4b, Ma3bc, Ma3b2, Ma2bcd, Ma2b2c, Mabcde -> c=7
    If n=6: Count is Ma6, Ma5b, Ma4bc, Ma4b2, Ma3bcd, Ma3b2c, Ma3b3, Ma2bcde, Ma2b2cd, Ma2b2c2, Mabcdef -> c=11
    If n=7: Count is Ma7, Ma6b, Ma5bc, Ma5b2, Ma4bcd, Ma4b2c, Ma4b3, Ma3bcde, Ma3b2cd, Ma3b2c2, Ma3b3c, Ma2bcdef, Ma2b2cde, Ma2b2c2d, Mabcdefg -> c=15

    (I may have missed something on n=7)

    In terms from n, what is the number (c) of these combinations produced for a certain value of n?
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    (Original post by Big-Daddy)
    In terms from n, what is the number (c) of these combinations produced for a certain value of n?
    Looks like this sequence

    Couldn't find an explict formula from a bit of googling, though you may have more luck.

    It can be defined with a second order recurrence relation, which would allow a recursive definiton for a computer. And with a bit of analysis, you should be able to relate it back to the sequence, to see how it arises.

    Edit: Struck out incorrect part of repsonse.
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    (Original post by ghostwalker)
    Looks like this sequence

    Couldn't find an explict formula from a bit of googling, though you may have more luck.

    It can be defined with a second order recurrence relation, which would allow a recursive definiton for a computer. And with a bit of analysis, you should be able to relate it back to the sequence, to see how it arises.
    Thanks for the response. That sequence looks precisely right. Doesn't it come with a function?

    (Original post by ghostwalker)
    It can be defined with a second order recurrence relation, which would allow a recursive definiton for a computer. And with a bit of analysis, you should be able to relate it back to the sequence, to see how it arises.
    So how would I go about doing this?
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    (Original post by Big-Daddy)
    Thanks for the response. That sequence looks precisely right. Doesn't it come with a function?
    Not that I'm aware of.

    So how would I go about doing this?
    I make the recurrence relation \displaystyle a_n=a_{n-1}+a_{n-2}-n+4

    Anything further, I'm afraid, you're going to have to research yourself, unless someone else on here can assist.


    Edit: On rechecking, that's not correct. So I don't know of a recurence relation.
 
 
 
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