Yes. 1 is both square and triangular.
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It is 13 squared, but it's not a triangular number
64
Add the previous triangular number. For example 6 + 3 or 10 + 6 or 15 + 10. Using some algebera: n(n+1)/2 + (n-1)n/2 = n-squared
squared
1, the first triangular number, is also a square.