a(n) = T(2n+1), where T(n) are the tribonacci numbers A000073.

Terms

a(0) =0a(1) =1a(2) =4a(3) =13a(4) =44a(5) =149a(6) =504a(7) =1705a(8) =5768a(9) =19513a(10) =66012a(11) =223317a(12) =755476a(13) =2555757a(14) =8646064a(15) =29249425a(16) =98950096a(17) =334745777a(18) =1132436852a(19) =3831006429a(20) =12960201916a(21) =43844049029a(22) =148323355432a(23) =501774317241