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:
“He bundles every forkful in its place,
And tags and numbers it for future reference,
So he can find and easily dislodge it
In the unloading. Silas does that well.
He takes it out in bunches like birds’ nests.”
—Robert Frost (1874–1963)