Yes, now it is much more clear. Since C={20-n1,c1-n2,c2-n3,c3-n4,c4-n5,c5-n6}
is the same as
C={20-n1, 20-n1- n2, 20-n1-n2- n3, 20-n1-n2-n3- n4, 20-n1-n2-n3-n4-n5, 20-n1-n2-n3-n4-n5-n6}
Then one way to do it is
A0 = {n1, n2, n3, n4, n5, n6};
B0 = 20;
C0 = B0 - Accumulate[A0] (* the excel equation *)
(* {20 - n1, 20 -n1-n2, 20 -n1-n2-n3, 20-n1-n2-n3- n4, 20-n1-n2-n3-n4-n5, 20-n1-n2-n3-n4-n5-n6} *)
Using numbers
A0 = {1, 2, 3, 4};
B0 = 20;
C0 = B0 - Accumulate[A0] (*the excel equation*)
(* {19, 17, 14, 10} *)