a(n) is the number of free polyominoes of width 3 and size n.

Terms

a(0) =1a(1) =3a(2) =8a(3) =23a(4) =71a(5) =193a(6) =490a(7) =1221a(8) =3011a(9) =7393a(10) =18025a(11) =43847a(12) =106206a(13) =256851a(14) =619642a(15) =1493272a(16) =3593527a(17) =8641624a(18) =20764212a(19) =49869733a(20) =119716469a(21) =287306693a(22) =689316717a(23) =1653539600a(24) =3965895220a(25) =9510880953a(26) =22806565004a(27) =54685294862a(28) =131116579494a(29) =314360235644