Question 133224
I don't claim to know much about matix algebra. But I do see a pattern.

To get the first of each successive row, take {{{4 * the outside number of the preceding row and add 2 * the inside number}}}.
To get the second number in the successive row, take {{{4 * the inside number of the preceding row and add 2* the outside number}}}

Thus, given (4,2,2,4) to get the second row, 
(4*4)+(2*2), (2*4)+(4*2),  (2*4)+(4*2), (4*4)+(2*2)
(20, 16, 16, 20)

To get the third row from the second row,
(4*20)+(2*16), (4*16)+(2*20),  (4*16)+(2*20), (4*20)+(2*16)
(112, 104, 104, 112)