finding formula for predictable sequence

lokeycmos

Joined Apr 3, 2009
431
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

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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thatoneguy

Joined Feb 19, 2009
6,349
With the exception of F(0)=1, F(n)=8n

lokeycmos

Joined Apr 3, 2009
431
With the exception of F(0)=1, F(n)=8n

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

Georacer

Joined Nov 25, 2009
5,154
Or even better: F(n)=8*n+δ(n)

lokeycmos

Joined Apr 3, 2009
431
Or even better: F(n)=8*n+δ(n)

what is that funky looking character after n+?

Georacer

Joined Nov 25, 2009
5,154
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.