The Fibonacci sequence in Java is a set of codes in the programming language that generates numbers starting with 0, 1 and 1, such that any subsequent number is the sum of the previous two. The fourth number in the sequence is 2, the sum of 1 and 1.

A Java program declares 0 and 1 and provides for user input of the number of Fibonacci values that should be calculated, such as the first 20 in the sequence. It will display on the screen the declared values first and calculate each one of the rest and print it step by step until the 20th.