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

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =17a(5) =66a(6) =181a(7) =508a(8) =1283a(9) =3664a(10) =10812a(11) =31171a(12) =88565a(13) =245524a(14) =692416a(15) =1968532a(16) =5609977a(17) =15928174a(18) =44982196a(19) =127190716a(20) =360208608a(21) =1021611491a(22) =2896270245a(23) =8202605953a(24) =23226285083a(25) =65780006703a(26) =186369631872a(27) =528047092459