My Math Forum formula remains true Fibonacci sequence

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 December 4th, 2011, 02:48 PM #1 Member   Joined: Dec 2011 Posts: 75 Thanks: 0 formula remains true Fibonacci sequence Hello! Fn+4 + Fn = 3Fn+2 for n = 0,1,2, . . . Would the formula, necessarily remain true if the sequence Fn is replaced by a sequence with the same recurrence relation as the Fibonacci sequence but different initial terms? Justify your answer briefly. any ideas? thanks
 December 4th, 2011, 03:04 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: formula remains true Fibonacci sequence Yes, the derivation of the given formula relies solely on the recurrence definition.

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### if tge sequence fn were replaced by a sequence with same recurrence relation as fibonacci but with diffrent initial terms

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