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 This took, 12.252, seconds .