An interesting pattern

Find a pattern in the following
1 squared is 1; 11 squared is 121; A difference of 120
2 squared is 4; 12 squared is 144; A difference of 140
3 squared is 9; 13 squared is 169; A difference of 160
4 squared is 16; 14 squared is 196; A difference of 180
5 squared is 25; 15 squared is 225; A difference of 200
Isn't interesting(For those who have a passion for math)?
This goes on ForeverThen, for numbers ending in the number 1(1,11,21,31...)
1 squared is 1
11 squared is 121
21 squared is 441
31 squared is 961
41 squared is 1681
51 squared is 2601
61 squared is 3721
71 squared is 5041
Now obviously, the ones digit is always 1. the Tens digit goes up by 2s, and the hundreds digit goes up 1,3,5,7,0,1,3
The reason behind this is
we are figuring out:(x + 10)² - x²
Expanding out you have
x² + 20x + 100 - x²= 100 + 20x
This matches exactly with your results which is 120, 140, 160, etc.
For your second sequence.Your numbers are of the form:10x + 1
Squaring you have:(10x + 1)²= 100x² + 20x + 1
The ones digit is always 1 because of the +1.The number goes up by 20 each time because of the +20x, which means the tens digit goes up by 2.The amount above 100 goes up by a square (plus the carry from the tens digit):0, 1, 4, 9, 16, 25(+1), 36(+1), 49(+1)the difference would be odd numbers, but it bumps up by the carry on every 5 numbers.1, 3, 5, 7, 9(+1)=10-->0, 1, 3, 5, 7, 9(+1)=10-->0