Given $N_1=26,~ N_2=20,~ N_3=4,~ N_4=16,~ N_5=10,~ N_6=2,$ and$N_1=26,~~ N_2=20,~~ N_3=4,~~ N_4=16,~~ N_5=10,~~ N_6=2,~$ and $N_7=14,$ and working backwards from
$N_8=8,$
which f'' found somewhere, I can reverse-engineer
\begin{align}N_1&=26~~\text{(seed value)}&N_4&=N_3+12&N_7&=N_6+12\\N_2&=N_1-6&N_5&=N_4-6&N_8&=N_7-6\\N_3&=N_2-2^4&N_6&=N_5-2^3&…\end{align}\begin{align}N_1&=26~~\text{(seed value)}&N_4&=N_3+12~~~&N_7&=N_6+12\\N_2&=N_1-6&N_5&=N_4-6&N_8&=N_7-6\\N_3&=N_2-2^4&N_6&=N_5-2^3&…\end{align}
… but that isn’t very satisfying. You could probably construct equally plausible derivations for lots of other answers.