Using elementary means, we derive an explicit formula for a3(n), the number of 3-core partitions of n, in terms of the prime factorization of 3n+1. Based on this result, we are able to prove several infinite families of arithmetic results involving a3(n), one of which specializes to the recent result of Baruah and Berndt which states that, for all n ≥ 0, a 3(4n+1)=a3(n).
- Jacobis Triple Product Identity
- Lambert series
- generating function