Abstract
A new recurrence for the number of subgroups of given index in the modular group is derived. The proof requires the derivation of a recurrence for a sequencea nbn from recurrences for thea n andb n. We show that this is always possible if thea n andb n satisfy polynomial recurrences. We also include a short proof of a result ofW. W. Stothers on the parity of the number of subgroups of given index in the modular group.
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