Fibonacci numbers in J

Example for versions j602

This example uses Binet’s formula.

g =: -: >: %:5 is equivalent to g =: 0.5 * (1 + 5 ^ 0.5) and assigns name g to value of golden ratio. %: extracts square root of the number, >: increments the number, -: divides the number by two. Operations are done from right to left, unless there are no parenthesis in the formula.

fibb=: (%:5) %~ g&^ -- (1-g)&^ is equivalent to fibb =: (0.2 ^ 0.5) * (g &^ -- (1-g) &^); this defines a formula for F(n) given the value of n. %~ is division, with dividend and divisor swapped.

i.16 generates numbers from 0 to 15, inclusive. 

load 'printf'

g=: -: >: %:5
fibb=: (%:5) %~ g&^ - (1-g)&^
fstr=: '...' ,~ ,~^:4 '%d, '
fstr printf fibb 1+i.16