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For N1=4, N2=5
S00 . . . .      
S01 S11 . . .      
S02 S12 S22 . .      
S03 S13 S23 S33 .      
. S14 S24 S34 S44      
. . S25 S35 S45      
. . . S36 S46      
. . . . S47      


Interchanged, skewed loop: 


for k2 := 0 to 8 do

  for k1 := $\max(0, K_2-3)$
to $\min(K_2, 4)$
do

S: A[k1,k2-k1] := A[k1-1,k2-k1]+A[k1,k2-k1-1]
That is, 

for k2 := 0 to 2N2-2 do

  for k1 := $\max(0, K_2-N_2+2)$
to $\min(K_2,N_1)$
do

S: A[k1,k2-k1] := A[k1-1,k2-k1]+A[k1,k2-k1-1]