Number of vertices with even distance from the root in "0-1-2" Motzkin trees on n edges.

Terms

a(0) =1a(1) =1a(2) =3a(3) =9a(4) =24a(5) =66a(6) =187a(7) =529a(8) =1506a(9) =4312a(10) =12394a(11) =35742a(12) =103377a(13) =299745a(14) =871011a(15) =2535873a(16) =7395522a(17) =21600720a(18) =63176964a(19) =185004852a(20) =542365407a(21) =1591631595a(22) =4675170690a(23) =13744341390a(24) =40438307599a(25) =119063564395a(26) =350799321531