Number of length-n gap-free words on {1,2,3}.

Terms

a(0) =1a(1) =3a(2) =7a(3) =21a(4) =67a(5) =213a(6) =667a(7) =2061a(8) =6307a(9) =19173a(10) =58027a(11) =175101a(12) =527347a(13) =1586133a(14) =4766587a(15) =14316141a(16) =42981187a(17) =129009093a(18) =387158347a(19) =1161737181a(20) =3485735827a(21) =10458256053a(22) =31376865307a(23) =94134790221a(24) =282412759267a(25) =847255055013