Given a b-multiplicative sequence and a prime p, studying the p-rarefaction consists in characterizing the asymptotic behaviour of the sums of the first terms indexed by the multiples of $p$. Under the "finiteness" assumption for the sequence, the integer values of the homogeneous "norm" 3-variate polynomial $\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2):=\prod_{j=1}^{p-1} (Y_0+\zeta_p^{i_1j}Y_1+\zeta_p^{i_2j}Y_2),$ where $i_1,i_2\in{1,2,...,p-1},$ and $\zeta_p$ is a primitive p-th root of unity, determine this asymptotic behaviour. It will be shown that a combinatorial method can be applied to $\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2).$ The method enables deducing functional relations between the coefficients as well as various properties of the coefficients of $\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2)$, in particular for $i_1=1, i_2=2,3.$ This method provides relations between binomial coefficients. It gives new proofs of the two identities $\prod_{j=1}^{p-1} (1-\zeta_p^j\right)=p$ and $\prod_{j=1}^{p-1} (1+\zeta_p^j-\zeta_p^{2j})=L_p$ (the p-th Lucas number). The sign and the residue modulo $p$ of the symmetric polynomials of $1+\zeta-\zeta_p^2$ can also be obtained. An algorithm for computation of coefficients of $\mathcal N_{p,i_1,i_2}(Y_0,Y_1,Y_2)$ is developed.
