Building periodic sequences from finite-support sequences
Thanks to @Florian's comments, here is sample solution

clc, clear
n = 0:1:7*10^6-1;
x = zeros(size(n));
x( find(n==1 | n==2 | n==3) ) = [(-1)^1*1 (-1)^2*2 (-1)^3*3];
y = x(mod(n,7)+1);
y = sum(reshape(y,7,[]),2)'


For large $k$s we have for example: y = 0    -1000000     2000000    -3000000           0           0           0.