Project 3 This programming project involves writing a program to calculate the terms of the following sequence of numbers: 0 1 2 5 12 29 . where each...

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 This programming project involves writing a program to calculate the terms of the following sequence of numbers: 0 1 2 5 12 29 ... where each term of the sequence is twice the previous term plus the second previous term. The 0th term of the sequence is 0 and the 1st term of the sequence is 1. 

For example: 

0 1 2 -> (0 + 1 + 2) + 2 = 5 0 1 2 5 -> (0 + 1 + 2 + 5) + 5 = 12 0 1 2 5 12 -> (0 + 1 + 2 + 5 + 12) + 12 = 29 … The interface to the program should be a GUI that looks similar to the following: