In [1]: N = 5
  
  In [2]: def skewed():
     ...:     for p in range(2, 2*N - 1):
     ...:         tmin = max(1, p - (N - 1))
     ...:         tmax = min((p + 1) // 2, N - 1)
     ...:         for t in range(tmin, tmax + 1):
     ...:             print("p: {} t: {} | a[{}][{}] = a[{}][{}] + a[{}][{}]".format(
     ...:                 p,
     ...:                 t,
     ...:                 p - t,
     ...:                 t,
     ...:                 p - t - 1,
     ...:                 t,
     ...:                 p - t,
     ...:                 t - 1,
     ...:             ))
  
  In [3]: def unskewed():
     ...:     for i in range(1, N):
     ...:         for j in range(1, min(i+2, N)):
     ...:              print("i: {} j: {} | a[{}][{}] = a[{}][{}] + a[{}][{}]".format(
     ...:                  i,
     ...:                  j,
     ...:                  i,
     ...:                  j,
     ...:                  i - 1,
     ...:                  j,
     ...:                  i,
     ...:                  j - 1,
     ...:              ))
  
  In [4]: unskewed()
  i: 1 j: 1 | a[1][1] = a[0][1] + a[1][0]
  i: 1 j: 2 | a[1][2] = a[0][2] + a[1][1]
  i: 2 j: 1 | a[2][1] = a[1][1] + a[2][0]
  i: 2 j: 2 | a[2][2] = a[1][2] + a[2][1]
  i: 2 j: 3 | a[2][3] = a[1][3] + a[2][2]
  i: 3 j: 1 | a[3][1] = a[2][1] + a[3][0]
  i: 3 j: 2 | a[3][2] = a[2][2] + a[3][1]
  i: 3 j: 3 | a[3][3] = a[2][3] + a[3][2]
  i: 3 j: 4 | a[3][4] = a[2][4] + a[3][3]
  i: 4 j: 1 | a[4][1] = a[3][1] + a[4][0]
  i: 4 j: 2 | a[4][2] = a[3][2] + a[4][1]
  i: 4 j: 3 | a[4][3] = a[3][3] + a[4][2]
  i: 4 j: 4 | a[4][4] = a[3][4] + a[4][3]
  
  In [5]: skewed()
  p: 2 t: 1 | a[1][1] = a[0][1] + a[1][0]
  p: 3 t: 1 | a[2][1] = a[1][1] + a[2][0]
  p: 3 t: 2 | a[1][2] = a[0][2] + a[1][1]
  p: 4 t: 1 | a[3][1] = a[2][1] + a[3][0]
  p: 4 t: 2 | a[2][2] = a[1][2] + a[2][1]
  p: 5 t: 1 | a[4][1] = a[3][1] + a[4][0]
  p: 5 t: 2 | a[3][2] = a[2][2] + a[3][1]
  p: 5 t: 3 | a[2][3] = a[1][3] + a[2][2]
  p: 6 t: 2 | a[4][2] = a[3][2] + a[4][1]
  p: 6 t: 3 | a[3][3] = a[2][3] + a[3][2]
  p: 7 t: 3 | a[4][3] = a[3][3] + a[4][2]
  p: 7 t: 4 | a[3][4] = a[2][4] + a[3][3]
  p: 8 t: 4 | a[4][4] = a[3][4] + a[4][3]

Actually writing it out like that really helped me grok what was going on, personally. If you look at the unskewed function then you can see that for every i there is a value for j that relies on the output from a previous j, e.g. the i: 1 j: 2 iteration uses a[1][1] which is the output from the i: 1 j: 1 iteration. But you can't find a similar example in the skewed function.