Named for the author of the Book of the Abacus, these numbers' successive ratios approach 1.618, the golden ratio.
These numbers can be obtained by the generating function "x" over quantity "1-x-x2", and a closed form expression of them is obtained from Binet's formula. The first two of these numbers are different from the first two Lucas numbers, but both sets satisfy the same recursion relation. Named for the author of the Book of the Abacus, these numbers' successive ratios approach 1.618, the golden ratio. They occur in the sums of diagonals in Pascal's Triangle and various places in nature such as the multiplication of rabbits. The nth of these is equal to the n minus 1st plus the n minus 2nd of them. For 10 points, name this sequence whose initial entries are 0, 1, 1, 2, 3, 5.
These numbers can be obtained by the generating function "x" over quantity "1-x-x2", and a closed form expression of them is obtained from Binet's formula.
 Fibonacci numbers or sequence