a(n) = C(n,1) + C(n,4) + ... + C(n, 3*floor(n/3) + 1).

Terms

a(0) =1a(1) =2a(2) =3a(3) =5a(4) =10a(5) =21a(6) =43a(7) =86a(8) =171a(9) =341a(10) =682a(11) =1365a(12) =2731a(13) =5462a(14) =10923a(15) =21845a(16) =43690a(17) =87381a(18) =174763a(19) =349526a(20) =699051a(21) =1398101a(22) =2796202a(23) =5592405a(24) =11184811a(25) =22369622a(26) =44739243a(27) =89478485a(28) =178956970a(29) =357913941