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Somehow a generalisation of the fibonacci numbers, do numbers created by the formula $ F(n) = F(n-1) + [F(n-1)-F(n-2)+F(n-3)-F(n-4)+F(n-5)-F(n-6).....]$ with $F(1) = 1$ have a specific name?

Paramar
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  • Your equation has two $F(n-1)$'s on the right. Did you mean that? For analogy with the Fibonacci sequences there should only be one. – Ross Millikan Mar 12 '14 at 20:55
  • Did you mean to write $F(n-1)$ twice? If you leave it out, the order 3 are usually called tribonacci, after that we just called them $n$-acci but I do not believe there is a standard accepted name http://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Fibonacci_numbers_of_higher_order – Will Jagy Mar 12 '14 at 20:55
  • Tribonacci, Tetrabonacci, Pentabonacci (ugh!), Fibonacci numbers of order $k$. – André Nicolas Mar 12 '14 at 20:59
  • yes I do mean it, but if only the factors between the [] are a known sequence , then it would be F(n-1) + that sequence – Paramar Mar 12 '14 at 21:42

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You need more starting terms than just one unless you define $F(0)$ and negative indices zero. If you did not intend $F(n-1)$ to be on the right twice, there are some values in Wikipedia, which has links into OEIS, this one for six on the right

Ross Millikan
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