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For nonnegative integers a, b, c and positive integer n, let N(a,b,c;n) denote the number of representations of n by the form ${\sum }_{i=1}^a(x{²}_i+x_i{y}_i+y{²}_i)+2{\sum }_{j=1}^b(u{²}_j+u_j{v}_j+v{²}_j)+4{\sum }_{k=1}^c(r{²}_k+r_k{s}_k+s{²}_k)$. Explicit formulas for N(a,b,c;n) for some small values were determined by Alaca, Alaca and Williams, by Chan and Cooper, by Köklüce, and by Lomadze. We establish formulas for N(2,1,0;n), N(2,0,1;n), N(1,2,0;n), N(1,0,2;n) and N(1,1,1;n) by employing the (p, k)-parametrization of three 2-dimensional theta functions due to Alaca, Alaca and Williams.