The Last of the 8s (Strange Adventures in Math)

Today I learned that I am one of the last of the 8s... I was born in 1978 and this year has a unique property that 19+78 = 97 the middle two numbers of the year 1978. Nifty. What other years have this?

Well assuming that we're just looking for years between 1000 and 10,000, we can write some python code to figure that out:

for i in range(1000,10000):
a = i/100
b = i%100
c = (i-(i/1000)*1000)/10
if (a+b == c):
  print(i)

This produces something kinda cool... but that I don't really understand:

1208
1318
1428
1538
1648
1758
1868
1978
2307
2417
2527
2637
2747
2857
2967
3406
3516
3626
3736
3846
3956
4505
4615
4725
4835
4945
5604
5714
5824
5934
6703
6813
6923
7802
7912
8901

That's 8 years that end in 8, 7 that end in 7, 6 that end in 6 etc down to one year that ends in 1 (8901). But where are the 9's? They're in adding the first value and the last value together. 36 of them (9*4?).. There's some other patterns in there as well. I'm sure there's a whole dissertation in mathematics that's been written on this, but I'm not even sure where to start searching for more info about it (it's the Loblaw principle... named after it's founder, Bob Loblaw..)