Here is a solution: ( 14 chars between {}s ).

sub c {(8**$_[0]-1)/7}
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Proof: For any x and n, by factoring, x**(n)-1 == (x-1)(x**(n-1)+x**(n-2)+...+1). So: x**(n-1)+x**(n-2)+...+1==(x**(n)-1)/(x-1). So, for x == 8: 8**(n-1)+8**(n-2)+...+1==(8**(n)-1)/7. And there, the left side is the sequence, the right side my solution.