a(n) is the number of free polyominoes of width 4 and size n.

Terms

a(0) =1a(1) =3a(2) =21a(3) =59a(4) =198a(5) =703a(6) =2568a(7) =8421a(8) =26165a(9) =78074a(10) =229881a(11) =668082a(12) =1928220a(13) =5523946a(14) =15745682a(15) =44666804a(16) =126251748a(17) =355692380a(18) =999498933a(19) =2802212026a(20) =7841587533a(21) =21907928927a(22) =61123152811a(23) =170333279738a(24) =474197771123