share/algebra/recur.transcript

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   3 (C49) CHAR(U(N+3)+6*U(N+2)+12*U(N+1)+8*U(N),0,U,N,3,[U(0)=1,U(1)=-2,U(2)=
   4 8]);
   5                                    2
   6                                   N    N           N
   7 (D52)                     U(N) = (-- - - + 1) (- 2)
   8                                   2    2
   9
  10 (C53) CHAR(U(N+1)-U(N),(1/6)*N*(N-1)*(N-2)+N-1,U,N,1,[U(0)=1]);
  11                                  3    2
  12                                 N    N    23 N   7
  13 (D58)                 U(N) = N (-- - -- + ---- - -) + 1
  14                                 24   4     24    4
  15
  16 (C59) CHAR(U(N+2)-2*U(N+1)+U(N),N**2,U,N,2,[U(0)=0,U(1)=1]);
  17                                     2
  18                                 2  N    N   5     5 N
  19 (D64)                   U(N) = N  (-- - - + --) + ---
  20                                    12   3   12     6
  21
  22 (C65) GENF(U(N+2)-U(N),2**N,U,N,2,[U(0)=1,U(1)=0]);
  23                                      N          N
  24                                     2    2 (- 1)
  25 (D71)                        U(N) = -- + --------
  26                                     3       3
  27
  28 (C72) CHAR(U(N+2)-4*U(N),3+2*N,U,N,2,[U(0)=1,U(1)=0]);
  29                                 N           N
  30                              7 2    25 (- 2)    2 N   13
  31 (D77)                 U(N) = ---- + --------- - --- - --
  32                               4        36        3    9
  33
  34 (C78) VARC1(U(N+1)-(N+1)*U(N),1,U,N,1,[U(0)=1]);
  35                                         N
  36                                        ====
  37                                        \       1
  38 (D79)                       U(N) = N!   >     ----
  39                                        /      I6!
  40                                        ====
  41                                        I6 = 0
  42
  43 (C80) VARC2(U(N+1)-(N+1)*U(N),1,U,N,1,[U(0)=1]);
  44                           N - 1           N
  45                           /===\          ====
  46                            ! !           \           1
  47 (D80)             U(N) = ( ! !  (I + 1))  >    -------------
  48                            ! !           /     I - 1
  49                           I = 1          ====  /===\
  50                                          I = 0  ! !
  51                                                 ! !  (J + 1)
  52                                                 ! !
  53                                                J = 1
  54
  55