MathDB

2017 Guts #19: Number of odd coefficients

Source:

February 21, 2017

algebra

Problem Statement

Find (in terms of

n \ge 1

) the number of terms with odd coefficients after expanding the product:

\prod_{1 \le i < j \le n} (x_i + x_j)

e.g., for

n = 3

the expanded product is given by

x_1^2 x_2 + x_1^2 x_3 + x_2^2 x_3 + x_2^2 x_1 + x_3^2 x_1 + x_3^2 x_2 + 2x_1 x_2 x_3

and so the answer would be

6