Arithmetic properties of bipartitions with designated summands

In 2002 Andrews, Lewis and Lovejoy introduced partition function PD(n), the number of partitions of n with designated summands and using modular forms they obtained many congruences modulo 3 and powers of 2. For example, they proved PD(3n+2)≡0(mod3). In this paper, we study various arithmetic properties of PD2(n) modulo 3 and powers of 2, where PD2(n) denotes the number of bipartitions of n with designated summands. We obtain congruences like PD2(3α+3(3n+2))≡0(mod3), PD2(3α+3(6n+4))≡0(mod3), PD2(24n+15)≡0(mod25), PD2(24n+23)≡0(mod25), PD2(24n+12)≡0(mod12) and PD2(18n+15)≡0(mod48). © 2016, Sociedad Matemática Mexicana.