HAPPY PI DAY!
I was doing some research on how a term in the Fibonacci sequence can be found, without generating all the previous terms, and I came across a very familiar sequence.
It's called the Padovan sequence.
Yes, the same as my 3MLS sequence, it carries on 1, 1, 2, 2, 3, 4, 5, 7, 9, ...
Yes, it can be expressed as Pn = Pn-2 + Pn-3.
Yes, there is a formula by which you can find a term in this sequence without generating all the previous terms.
I recommend the following pages:
http://mathworld.wolfram.com/PadovanSequence.html
http://people.bath.ac.uk/abscjkw/LectureNotes/Padovan.pdf
Fortunately for me, I have yet to see this Padovan sequence described with a population model. So, my contribution (should I actually be the first to do this) is of describing the Padovan sequence with a population model similar to that of Fibonacci's.
I was doing some research on how a term in the Fibonacci sequence can be found, without generating all the previous terms, and I came across a very familiar sequence.
It's called the Padovan sequence.
Yes, the same as my 3MLS sequence, it carries on 1, 1, 2, 2, 3, 4, 5, 7, 9, ...
Yes, it can be expressed as Pn = Pn-2 + Pn-3.
Yes, there is a formula by which you can find a term in this sequence without generating all the previous terms.
I recommend the following pages:
http://mathworld.wolfram.com/PadovanSequence.html
http://people.bath.ac.uk/abscjkw/LectureNotes/Padovan.pdf
Fortunately for me, I have yet to see this Padovan sequence described with a population model. So, my contribution (should I actually be the first to do this) is of describing the Padovan sequence with a population model similar to that of Fibonacci's.
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