finding formula for predictable sequence

Discussion in 'Math' started by lokeycmos, Dec 10, 2011.

  1. lokeycmos

    Thread Starter Active Member

    Apr 3, 2009
    432
    7
    OK, so many years ago when i was in juvey i had lots of time on my hands. i used to find predictable sequences of numbers such as fibonacci sequence. i would rack my mind to find a formula to find any number in the sequence given x. x would be the location of the number in the sequence. for example the formula for the fibonacci sequence is: (i didnt come up with this myself, its just an example)

    Fib(n) = 1.6180339..n – (–0.6180339..)n[​IMG][​IMG]
    2.236067977..​


    well, i have really lost my touch and looking for help with a sequence i thought of last night when my mind was expanded. i attached a pic.
    the sequence is 1,8,16,24,32,40......
    just wondering if someone could help me find the formula? this is not homework or anything just something that popped in my mind last night. TY
     
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  2. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
    718
    With the exception of F(0)=1, F(n)=8n
     
  3. lokeycmos

    Thread Starter Active Member

    Apr 3, 2009
    432
    7

    OMG! that was super easy! cant believe i missed that! i really lost my touch.
     
  4. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Or even better: F(n)=8*n+δ(n)
     
  5. lokeycmos

    Thread Starter Active Member

    Apr 3, 2009
    432
    7

    what is that funky looking character after n+?
     
  6. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    It is the Greek letter delta, symbolizing the delta (dirac) function. Look it up in Wikipedia.

    For discrete time it is defined as δ(n)=0 for n<>0 and δ(0)=1.

    For continuous time, is has the property that \int^{e}_{-e}\delta(t)dt=1, where e is an arbitrarily small number.
     
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