Fibonacci Numbers
The Fibonacci numbers are the archetype of a linear, homogeneous recurrence relation with constant coefficients (see below). They are defined using the linear recurrence relation
with seed values:
Explicitly, recurrence yields the equations:
etc.
We obtain the sequence of Fibonacci numbers which begins:
- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
It can be solved by methods described below yielding the closed-form expression which involve powers of the two roots of the characteristic polynomial t2 = t + 1; the generating function of the sequence is the rational function
Read more about this topic: Recurrence Relation
Famous quotes containing the word numbers:
“Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.”
—Gore Vidal (b. 1925)