A linearly recursive sequence in n variables is a tableau of scalars for i1,i2,…, in ⩾ 0, such that for each 1 ⩽ i ⩽ n, all rows parallel to the ith axis satisfy a fixed linearly recursive relation hi(x) with constant coefficients. We show that such a tableau is Hadamard invertible (i.e., the tableau is linearly recursive) if and only if all , and each row is eventually an interlacing of geometric sequences. The procedure is effective, i.e., given a linearly recursive sequence , it can be tested for Hadamard invertibility by a finite algorithm. These results extend the case n = 1 of Larson and Taft.
