a(2)=1; for n>2, a(n) = A109742(n)/3.

Terms

a(0) =1a(1) =3a(2) =9a(3) =41a(4) =231a(5) =1551a(6) =12037a(7) =105861a(8) =1039539a(9) =11268059a(10) =133585089a(11) =1718984673a(12) =23857531519a(13) =355190381031