Number of rooted ordered trees where no branch is identical to its adjacent neighbor.

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =6a(5) =16a(6) =45a(7) =128a(8) =371a(9) =1106a(10) =3343a(11) =10230a(12) =31635a(13) =98714a(14) =310366a(15) =982437a(16) =3128051a(17) =10011848a(18) =32193840a(19) =103955571a(20) =336946034a(21) =1095873115a(22) =3575319049a(23) =11697938232a(24) =38374479841a(25) =126190075741a(26) =415889689954