Number of length-n 0..2 arrays with no adjacent pair x,x+1 repeated.

Terms

a(0) =3a(1) =9a(2) =27a(3) =79a(4) =225a(5) =626a(6) =1710a(7) =4605a(8) =12259a(9) =32320a(10) =84504a(11) =219356a(12) =565816a(13) =1451349a(14) =3704271a(15) =9412153a(16) =23818707a(17) =60055275a(18) =150913073a(19) =378064818a(20) =944442242a(21) =2353140149a(22) =5848794543a(23) =14504575980a(24) =35894673012a(25) =88654500384a(26) =218560230944