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Thread: Triple Fibonacci Recursion

  1. #1 Triple Fibonacci Recursion 
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    I'm certain the sequence for the recursive rule above is already popularized under some name (so what is it?)

    Interesting properties? What about an explicit formula (I'm sure it'll include too)


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  3. #2  
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    Root 1 Root 2 Root 3 S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
    0 0 1 1 2 4 6 12 22 40 74 136 250
    0 1 0 1 2 3 6 11 20 37 68 125 230
    1 0 0 1 1 2 4 7 13 24 44 81 149
    1 5 10 16 31 57 104 192 353 649 1194 2196 4039
    1 2 3 6 11 20 37 68 125 230 423 778 1431



    :P


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  4. #3  
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    Never mind. Tribonacci numbers (how did I not catch that?).
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  5. #4  
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    A systematic way to get explicit expressions out of a recursion relation is the z-transform: Z-transform - Wikipedia, the free encyclopedia
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