We define a sequence by recursion: $$a_{2n}=a_{n}+a_{3n-1}$$ $$a_{3n}=a_{2n-1}+a_{4n+3}$$ $$a_{4n}=a_{3n-2}+a_{2n+1}-a_{n+7}$$
Question: Does each term of this sequence equal to zero?
I have proved $a_1=a_2=a_3=...=a_{17}=0$.
Does each term of this sequence equal to zero?
2
$\begingroup$
sequences-and-series
recurrence-relations
recursion
-
0I don't even know the value of $a_{18}$. – 2017-02-12
-
0Well yes they are all 0 – 2017-02-12
-
1How did you prove it? – 2017-02-12