Is it possible that the number of $\mathcal{T}$-algebras is an arithmetic progression?
Here is a near miss: Let $\mathcal{V}$ be the variety of $\mathbb Z_2$-sets. These are the algebras $\langle X; \alpha(x)\rangle$ with a single unary operation $\alpha(x)$ such that $\alpha^2(x)=x$. The number of isomorphism types of algebras of size $n$ in this variety is $t_n=\big\lfloor\frac{1}{2} n\big\rfloor+1$.