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total number of valence electrons of group 18 ions

Result

sum_(k=0)^({0, 6, 6, 6, 4, 2, 18}) x^k = {1, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^4 + x^3 + x^2 + x + 1, x^2 + x + 1, x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1}
sum_(k=0)^({0, 6, 6, 6, 4, 2, 18}) x^k = {1, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, x^4 + x^3 + x^2 + x + 1, x^2 + x + 1, x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1}

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