A066115 (OEIS)

A066115 in the OEIS is a sequence listing the number of partitions of an integer \( n \) into distinct parts where all parts are congruent to 1 modulo 3 (meaning each part leaves a remainder of 1 when divided by 3). For example, for \( n = 5 \), the sequence counts how many ways to write 5 as sums of unique numbers like 1, 4, etc., with each number fitting the criterion. This sequence explores specialized forms of integer partitions constrained by both the size and modular conditions, providing insight into the structure of these specific additive decompositions.