total number of valence electrons of group 1 ions

sum_(k=0)^({0, 0, 0, 2, 0, 8, 0, 2}) x^k = {1, 1, 1, x^2 + x + 1, 1, x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 1, x^2 + x + 1}