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Tridiagonal determinant recurrence

For diagonal entries

a_{i}

, superdiagonal entries

b_{i}

, and subdiagonal entries

c_{i}

, the leading principal determinants satisfy

d_{n} = a_{n} d_{n - 1} - b_{n - 1} c_{n - 1} d_{n - 2}, d_{0} = 1, d_{1} = a_{1} .

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