Abstract
The notion of the generalized Fibonacci matrix <TEX>$\mathcal{F}_n^{(a,b,s)}$</TEX> of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix <TEX>$\mathcal{F}_n^{(a,b,-1)}$</TEX> is derived. Correlations between the matrix <TEX>$\mathcal{F}_n^{(a,b,-1)}$</TEX> and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.
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