Build a staircase for my kid
Python 2, 55 bytes



i=2
exec"print(i%2*' '+`2%i*1122`*i)[:i];i+=1;"*input()


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Cycles between blocks of 22, 44, except the top row is 00. For example, on input 10, prints

00
 22
2244
 2244
224422
 224422
22442244
 22442244
2244224422
 2244224422


Prints rows of increasing length i=2,3,.. by creating a space for odd lengths, repeating the pattern i times, and trunctating to length i. The pattern is 2244 for all rows except the first one i=2 for which it's 0. This is achieved with the arithmetic expression 2%i*1122.