Question: Is The rational function that belongs to  the C-finite sequence,

    [[2, 10, 36, 145], [2, 7, 2, -1]], namely

                                           2    3
                              2 + 6 t + 2 t  - t
                           --------------------------
                                        2      3    4
                           1 - 2 t - 7 t  - 2 t  + t

   the Hadamard product of two rational functions of (denominator) degree 2?

                                 Answer: , true

Question: Is the generating function for the number of perfect matchings in \
    a 4 by n rectangle, i.e.

                                 (1 + t) (t - 1)
                           - -----------------------
                                 2            3    4
                             -5 t  - t + 1 - t  + t

the Hadamard product of two rational functions, each of (denominator) degree\
     2?

                                 Answer: , true

Question: Is the generating function for the number of perfect matchings in \
    a 8 by n rectangle, i.e.

              8        9       3       2        4       11    14         6
- (-1 - 1033 t  + 110 t  + 26 t  + 43 t  - 360 t  - 26 t   + t   + 1033 t

           12        5        10    /   16    15       14       13        12
     - 43 t   - 110 t  + 360 t  )  /  (t   - t   - 76 t   - 69 t   + 921 t
                                  /

            11         10        9         8        7         6        5
     + 584 t   - 4019 t   - 829 t  + 7012 t  - 829 t  - 4019 t  + 584 t

            4       3       2
     + 921 t  - 69 t  - 76 t  - t + 1)

the Hadamard product of four rational functions, each of (denominator) degre\
    e 2?

                                 Answer: , true

Question: Is the generating function for the number of perfect matchings in \
    a 10 by n rectangle, i.e.

             2        3         4         5           6          7            8
- (-1 + 197 t  + 214 t  - 9741 t  - 7262 t  + 202037 t  + 56736 t  - 2064705 t

               9            11             14             12             10
     + 156848 t  - 2972710 t   + 54699758 t   - 32425754 t   + 11058754 t

                 16             15             13    30        28        27
     - 54699758 t   - 15137114 t   + 10324398 t   + t   - 197 t   + 214 t

             26           24         25             17            19
     + 9741 t   - 202037 t   - 7262 t   + 10324398 t   - 2972710 t

                 18             20            22           21          23    /
     + 32425754 t   - 11058754 t   + 2064705 t   + 156848 t   + 56736 t  )  /
                                                                           /

                   2        3          4          5           6           7
    (-t + 1 - 285 t  - 411 t  + 18027 t  + 20689 t  - 472275 t  - 271027 t

                8           9             11              14              12
     + 6149853 t  + 471319 t  + 10402780 t   - 335484428 t   + 157353820 t

                 10              16              15             13        30
     - 42303393 t   + 429447820 t   + 123321948 t   - 58545372 t   - 285 t

              28          27           26            24           25
     + 18027 t   - 20689 t   - 472275 t   + 6149853 t   + 271027 t

                  17             19              18              20
     - 123321948 t   + 58545372 t   - 335484428 t   + 157353820 t

                 22             21           23    32        29    31
     - 42303393 t   - 10402780 t   - 471319 t   + t   + 411 t   + t  )

the Hadamard product of five rational functions, each of (denominator) degre\
    e 2?

                                 Answer: , true

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