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Fade sequence (Posted on 2005-10-26) Difficulty: 4 of 5
Find the next few terms:
1,2,5,12,28,66,155,364,855,2008,4716


Hint: It's not quite Fibonacccci
more like FibonaCCcci

  Submitted by Larry    
Rating: 3.0000 (3 votes)
Solution: (Hide)
11076, 26013, 61094

a(n)=2*a(n-1)+1*a(n-2)+0*a(n-3)+(-1)*a(n-4)

In Fibonacci, each term is a function of the previous 2 terms.
The misspelling in the hint, with the letter "c" appearing 4 times was meant to suggest that each term is a function of the previous 4 terms, of the form:
a(n)=W*a(n-1)+X*a(n-2)+Y*a(n-3)+Z*a(n-4)

Once that assumption is made, the reasoning is straightforward.

One can assume that the second term "2" is a function of 0,0,0,1 and therefore "W" must be 2.
Then the 3rd term "5" must be a function of 0,0,1,2, and so "X" must be 1 since 5=2*2 + 1*1
And the 4th term "12" must be a function of 0,1,2,5 and so "Y" must be zero since 12=2*5 + 1*2 + 0*1
Finally the 5th term "28" must be a function of 1,2,5,12 and so "Z" must be (-1) since 28=2*12 + 1*5 + 0*2 + (-1)*1

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: a solutionLarry2005-10-27 00:51:36
re(2): a solutionSilverKnight2005-10-26 14:24:30
re: a solutionCharlie2005-10-26 14:23:00
Solutiona solutionSilverKnight2005-10-26 13:26:56
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