I have a 5-term recurrence relation of the form: $$\alpha_n a_{n-3} + \beta_n a_{n-2} + \gamma_n a_{n-1} + \delta_n a_{n} + \rho_n a_{n+1} =0 .$$ How can I rewrite this, as a 3-term recurrence relation? i.e. how to rewrite in the form $$\bar{\alpha}_n a_{n-1} + \bar{\beta}_n a_{n} + \bar{\gamma}_n a_{n+1} =0$$.
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2I don't think you can do this in general. – lhf Feb 06 '19 at 13:49
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if the coefficient sequences are constant and the resulting characteristic polynomial reduces as a cubic times a quadratic, something nice does happen. – Will Jagy Feb 06 '19 at 15:49