05AB1E, 19 bytes

[¼¾ENnN+N·¾[¼¾ENnN+¾N·¾-1‚ß¾*1‚ß*-,

Port of @alephalpha's Haskell answer.

Outputs indefinitely.

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Explanation:

[                   # Loop indefinitely:
 ¼                  #  Increase variable `c` by 1 (0 by default)
  ¾E                #  Inner loop `N` in the range [1,`c`]:
    NnN+         #   Push N²+N
 , #  N·¾- Pop and output:
    NnN+¾N·¾-1‚ß*-  #   Push N²+N-c*min(2N-c,1)
    Nn     1‚ß         #   Pop andN²
 push min(2N    N+            #      +N
                 -c,1)  #        -
        ¾   ¾*    *   #   Multiply by `c`:    c*
             1‚ß    #           min(2N-c    ,1)*c
         N·    -     #   Subtract: N²+N-min(           2N-c,1)*c
           ¾-    ,   #   Pop and output it with trailing newline        -c