No, never was a BN3. The models were:
BN-2A Mk III-1: First production version, with short nose.
BN-2A Mk III-2: Lengthened nose and higher operating weight.
BN-2A Mk III-3: Variant certified for operation in the United States.
BN-2A Mk III-4III-2: fitted with 350 lb rocket-assisted takeoff equipment.
BN-2A Mk III-5III-2: with sound-proofed cabin, modernised cockpit/interior and new engines (proposed, unbuilt as yet).
Trislander M: Proposed military version, not built.
72 were built.