How do you know which numbers come next?
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The way you get to the next number in the sequence is to add the previous two numbers together, and add what term it is in the sequence (where we suppose it starts at the -1st term). In other words, a(n)=a(n−1)+a(n−2)+n, where a(−1)=a(0)=1 and start the recurrence. So a(1)=a(0)+a(−1)+1=1+1+1=3.
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