Let λ = (λi)i ≥ 1, μ = (μi)i ≥ 1, ν = (νi)i ≥ 1, ω = (ωi)i ≥ 1 and ψ = (ψi)i ≥ 1 be given sequences, and let (ai,j)i,j ≥ 1 be the doubly indexed sequence given by the recurrence [Formula: see text](i ≥ 3, j ≥ 2), with various choices for the two first rows a1,j, a2,j and first column ai,1. Note that the coefficients depend on the row index only. In this article we study the principal minors of doubly indexed sequences (ai,j)i,j ≥ 1 for certain sequences and certain initial conditions. Moreover, let (bi,j)i,j ≥ 1 be the doubly indexed sequence given by the recurrence [Formula: see text] with various choices for the first row b1,j and first column bi,1. We also study the principal minors of doubly indexed sequence (bi,j)i,j ≥ 1.

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