Magic sequence

Johnny has invented a magic sequence. Each element of the sequence is defined by the same recursive definition - take some linear combination of previous elements (whose coefficients are fixed) and add to them the n-th powers of some integers. Formally: Xn = Xn-1*a1 + ... + Xn-i*ai + b1*d1n + ... + bj*djn, for some integer constants p,q,a1,...,ap,b1,..., bq,d1,..., dq. Of course, as the values can