Number of tilings of a 5 X n rectangle using n pentominoes of shapes P, I, X.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =13a(5) =52a(6) =123a(7) =366a(8) =909a(9) =2444a(10) =7108a(11) =19157a(12) =53957a(13) =146826a(14) =400704a(15) =1115852a(16) =3059907a(17) =8475420a(18) =23369304a(19) =64225984a(20) =177572352a(21) =488839323a(22) =1349102071a(23) =3722419367a(24) =10255126169a(25) =28303059509a(26) =78013005366a(27) =215160477217a(28) =593488173404