Number of tilings of a 3 X n rectangle with n trominoes.

Terms

a(0) =1a(1) =1a(2) =3a(3) =10a(4) =23a(5) =62a(6) =170a(7) =441a(8) =1173a(9) =3127a(10) =8266a(11) =21937a(12) =58234a(13) =154390a(14) =409573a(15) =1086567a(16) =2882021a(17) =7645046a(18) =20279829a(19) =53794224a(20) =142696606a(21) =378522507a(22) =1004078871a(23) =2663452699a(24) =7065162260a(25) =18741269167a(26) =49713692146a(27) =131872134232a(28) =349808216915a(29) =927912454723