The Representations by Certain Duodenary Quadratic Forms

The determination of the number of representations of a positive integer by certain quadratic forms is an important goal of number theory. Formulae for N(12i, 22j, 32k, 62l; n) for the nine octonary quadratic forms appear in the literature, whose coefficients are 1, 2, 3 and 6. Here, we determine formulae, for the numbers of representations of a positive integer by one hundred and six different duodenary quadratic forms whose coefficients are 1, 2, 3 and 6.