Question Number 186688 by norboyev last updated on 08/Feb/23
$${a}_{\mathrm{1}} =\mathrm{0} \\ $$$${a}_{\mathrm{2}} =\mathrm{1} \\ $$$${a}_{{n}+\mathrm{2}} ={a}_{{n}+\mathrm{1}} −{a}_{{n}} \\ $$$${a}_{\mathrm{885}} =? \\ $$
Commented by mr W last updated on 08/Feb/23
$$\begin{array}{|c|c|}{{n}}&\hline{\mathrm{0}}&\hline{\mathrm{1}}&\hline{\mathrm{2}}&\hline{\mathrm{3}}&\hline{\mathrm{4}}&\hline{\mathrm{5}}&\hline{\mathrm{6}}&\hline{\mathrm{7}}&\hline{\mathrm{8}}&\hline{\mathrm{9}}\\{{a}_{{n}} }&\hline{\mathrm{0}}&\hline{\mathrm{1}}&\hline{\mathrm{1}}&\hline{\mathrm{0}}&\hline{−\mathrm{1}}&\hline{−\mathrm{1}}&\hline{\mathrm{0}}&\hline{\mathrm{1}}&\hline{\mathrm{1}}&\hline{\mathrm{0}}\\\hline\end{array} \\ $$$${a}_{\mathrm{3}{n}} =\mathrm{0} \\ $$$${a}_{\mathrm{3}{n}+\mathrm{1}} =\left(−\mathrm{1}\right)^{{n}} \\ $$$${a}_{\mathrm{3}{n}+\mathrm{2}} =\left(−\mathrm{1}\right)^{{n}} \\ $$$$\Rightarrow{a}_{\mathrm{885}} ={a}_{\mathrm{3}×\mathrm{295}} =\mathrm{0} \\ $$