[tex]\displaystyle \bf \\
\text{\bf Avem sirul: }\\
1,~5,~7,~17,~31,~65,~127 \hdots\\
\text{\bf Observam ca:} \\
7 = 2\times 1 + 5\\
17 = 2\times 5 + 7\\
31 = 2\times 7 + 17\\
{\bf s.a.m.d.}
\text{\bf Rezulta ca termenul general este: } \\
\boxed{\bf a_n = 2\times a_{n-2} + a_{n-1}}~~~n \geq 3
[/tex]