symbolic summation with integer division

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Can sage handle symbolic summation with integer division? looks like neither // nor int() handles symbolic expression.

Example:

x,n = var('x,n')
sum(x//3,x,0,n)

or

sum(3*x, x, 0, int(n/3)-1) + (n%3+1)*(n//3)

(above 2 are equivalent)