Vector Space
The term Fibonacci sequence is also applied more generally to any function g from the integers to a field for which g(n+2) = g(n) + g(n+1). These functions are precisely those of the form g(n) = F(n)g(1) + F(n-1)g(0), so the Fibonacci sequences form a vector space with the functions F(n) and F(n-1) as a basis.
More generally, the range of g may be taken to be any abelian group (regarded as a Z-module). Then the Fibonacci sequences form a 2-dimensional Z-module in the same way.
Read more about this topic: Generalizations Of Fibonacci Numbers
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