For starters, why use symsum at all? Doesn't sum() do exactly what is needed?
L(t) = 1 + sum(0.5.^(abs(k-5).*V(t)))./sum(0.5.^(abs(k-5)));
I suspect other optimizations can be made as well. For sure, pre-allocate L. But for only 12054 elements, this loop may be fast enough for what's needed.