Non-recursive formula

  • Thread starter flying2000
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Main Question or Discussion Point

How to get a non-recursive formula for y(n):

y(n)=1 (n=1 or 2)
y(n)=0 (n=3 or 4)
y(n)=(y(n-4) + y(n-3))/2


Any hints apprecaited..
 

Answers and Replies

  • #2
matt grime
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write down the first few terms, guess an answer and prove it inductively, that'd be my guess.

or work backwards from y(n) repeatedly subs'ing in and see what works.
 
  • #3
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I have already wrote down previous 20 items, still can't find the relationship

I have already wrote down previous 20 items, still can't find the relationship


matt grime said:
write down the first few terms, guess an answer and prove it inductively, that'd be my guess.

or work backwards from y(n) repeatedly subs'ing in and see what works.
 
  • #4
matt grime
Science Advisor
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Ok, I suppose a 4th order is going a little too far to ask you to spot it...

however, it is linear and homogeneous, so the general solution is of the form At^n for some constants t and A, t satisfies

t^n = t^{n-4}+t^{n-3}

or

t^4=1+t,

solve that, to get 4 solutions, and then apply the 4 initial conditions.
 

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