Pythagorean Triples

My formulas are
1.2n + 1
2.2n2 + 2n
3.2n2 + 2n + 1
4.4n2 + 6n + 2
5.2n3 + 3n2 + n
To get these formulas I did the following
1.Take side 'a' for the first five terms 3, 5, 7, 9, 11. From these numbers you can see that the formula is 2n + 1 because these are consecutive odd numbers (2n + 1 is the general formula for consecutive odd numbers) You may be able to see the formula if you draw a graph
2.From looking at my table of results, I noticed that 'an + n = b'. So I took my formula for 'a' (2n + 1) multiplied it by 'n' to get '2n2 + n'. I then added my other 'n' to get '2n2 + 2n'. This is a parabola as you can see from the equation and also the graph.
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