sum of result circular convolution vector

Question

I am wondering if there is a simple way of finding the sum of the circular convolution vector? i.e. not brute force

for example:

if d = circ_conv(c, c), then (sum of the elements in d) = (sum of elements in c)^2

if x = [1,2,3,...,100], and h=[1,1,2,2], is there a similar formula for calculating the sum of elements in d=circ_conv(x,h). (d = 30300).

Thank you!