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The Quartus U(1,1)F
The series around U_{0}:
 The quartus is symmetric with regard to U_{0}U_{1}. It can be derived from the primus by taking the subsequent sums of U_{n+1} and U_{n} of that series (with U_{0} = u_{0}+u_{1} = 1).

The quartus coefficients matrix
Disregarding signs, this matrix is identical to the tertius coefficients matrix.
The degree of a polynome is one less than its index.
Exponents decrease with steps of 1.
Note that the columns come in pairs with an index shift.
U_{1}:  1  
U_{2}:  1  1  
U_{3}:  1  1  1  
U_{4}:  1  1  2  1  
U_{5}:  1  1  3  2  1  
U_{6}:  1  1  4  3  3  1  
U_{7}:  1  1  5  4  6  3  1  
U_{8}:  1  1  6  5  10  6  4  1  
U_{9}:  1  1  7  6  15  10  10  4  1  
U_{10}:  1  1  8  7  21  15  20  10  5  1  
U_{11}:  1  1  9  8  28  21  35  20  15  5  1  
U_{12}:  1  1  10  9  36  28  56  35  35  15  6  1  
U_{13}:  1  1  11  10  45  36  84  56  70  35  21  6  1  
U_{14}:  1  1  12  11  55  45  120  84  126  70  56  21  7  1  
U_{15}:  1  1  13  12  66  55  165  120  210  126  126  56  28  7  1  
U_{16}:  1  1  14  13  78  66  220  165  330  210  252  126  84  28  8  1  
U_{17}:  1  1  15  14  91  78  286  220  495  330  462  252  210  84  36  8  1  
U_{18}:  1  1  16  15  105  91  364  286  715  495  792  462  462  210  120  36  9  1  
U_{19}:  1  1  17  16  120  105  455  364  1001  715  1287  792  924  462  330  120  45  9  1  
U_{20}:  1  1  18  17  136  120  560  455  1365  1001  2002  1287  1716  924  792  330  165  45  10  1  
U_{21}:  1  1  19  18  153  136  680  560  1820  1365  3003  2002  3003  716  1716  792  495  165  55  10  1  
U_{22}:  1  1  20  19  171  153  816  680  2380  1820  4368  3003  5005  3003  3432  1716  1287  495  220  55  11  1  
U_{23}:  1  1  21  20  190  171  969  816  3060  2380  6188  4368  8008  5005  6435  3432  3003  1287  715  220  66  11  1  
U_{24}:  1  1  22  21  210  190  1140  969  3876  3060  8568  6188  12376  8008  11440  6435  6435  3003  2002  715  286  66  12  1  
U_{25}:  1  1  23  22  231  210  1330  1140  4845  3876  11628  8568  18564  12376  19448  11440  12870  6435  5005  2002  1001  286  78  12  1  
U_{26}:  1  1  24  23  253  231  1540  1330  5985  4845  15504  11628  27132  18564  31824  19448  24310  12870  11440  5005  3003  1001  364  78  13  1 