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

 

With the exception of F(0)=1, F(n)=8n

 

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.

 

Or even better: F(n)=8*n+δ(n)

 

Or even better: F(n)=8*n+δ(n)

what is that funky looking character after n+?

 

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.