Sandbox

$H_q(\mathbb{Z}/p\mathbb{Z}\oplus \mathbb{Z}/p\mathbb{Z};M)=\{\begin{array}{cc}(M/pM{)}^{(q+3)/2}\oplus ({\mathrm{A}}_{\mathrm{n}}(p){)}^{(q-1)/2},& q=1,3,5,\dots \\ (M/pM{)}^{q/2}\oplus ({\mathrm{A}}_{\mathrm{n}}(p){)}^{(q+2)/2},& q=2,4,6,\dots \\ M,& q=0\\ \end{array}$