Number of n-bead bracelets using exactly three colors with no adjacent beads having the same color.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =3a(5) =10a(6) =9a(7) =27a(8) =29a(9) =75a(10) =93a(11) =221a(12) =315a(13) =684a(14) =1095a(15) =2247a(16) =3855a(17) =7682a(18) =13797a(19) =27009a(20) =49939a(21) =96906a(22) =182361a(23) =352695a(24) =671091a(25) =1296855a(26) =2485533a(27) =4806075a(28) =9256395a(29) =17920857