Hello,
One solution may be
[tex] a_{n+1}=a_{n}*(-3) +1 [/tex]
[tex] a_{0}=\frac{1}{3} [/tex]
[tex] a_{1}=\frac{1}{3}*(-3) +1=0 [/tex]
[tex] a_{2}=0*(-3) +1=1 [/tex]
[tex] a_{3}=1*(-3) +1=-2 [/tex]
[tex] a_{4}=(-2)*(-3) +1=7 [/tex]
[tex] a_{5}=7*(-3) +1=-20 [/tex]
[tex] a_{6}=(-20)*(-3) +1=61 [/tex]
...
REM:
[tex] a_{n}=\frac{(-3)^{n}}{12}+\frac{1}{4} [/tex]
