The ordinary partition function p(n) counts the number of representations of a positive integer n as the sum of positive integers. We denote by p3(n) the number of partitions of n with no parts divisible by 3: We demonstrate congruence relations for arithmetic sequences qn+(2q2-2)/24 where q is a prime other than 3 congruent to 3 (mod 4): We also prove a result when q = 5 and make a conjecture about a generalization .
Utgof, Naomi, "A Restricted Partition Function Modulo 3" (2002). Mathematical Sciences Technical Reports (MSTR). 59.