The Triangular Numbers
The triangular numbers are: 1, 3, 6, 10, 15, 21, 28, ...

The pattern is made clear by writing down what we have to add to each number to get the next: 

1   3   6   10   15   21 ...
  2   3   4    5    6    7 ...
Let's store the triangular number in T and the bit we add on in A - it will have to be increased by ONE each time.
  1. Load T with ONE
  2. Load A with TWO
  3. Output T
  4. Add A to T
  5. Increment A
  6. Go to step 3 

 LDA #1
 STA T
 LDA #2
 STA A
LOOP: OUT T
 LDA T
 ADD A
 STA T
 INC A
 JMP LOOP

LDA #1
STA T
LDA #2
STA A
LOOP: OUT T
LDA T
ADD A
STA T
INC A
JMP LOOP

Assembler