The Filbert Matrix
نویسندگان
چکیده
A Filbert matrix is a matrix whose (i, j) entry is 1/Fi+j−1, where Fn is the n Fibonacci number. The inverse of the n × n Filbert matrix resembles the inverse of the n× n Hilbert matrix, and we prove that it shares the property of having integer entries. We prove that the matrix formed by replacing the Fibonacci numbers with the Fibonacci polynomials has entries which are integer polynomials. We also prove that certain Hankel matrices of reciprocals of binomial coefficients have integer entries, and we conjecture that the corresponding matrices based on Fibonomial coefficients have integer entries. Our method is to give explicit formulae for the inverses.
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