a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k-1,k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =3a(5) =5a(6) =7a(7) =12a(8) =21a(9) =34a(10) =55a(11) =92a(12) =153a(13) =251a(14) =414a(15) =686a(16) =1133a(17) =1869a(18) =3088a(19) =5103a(20) =8427a(21) =13917a(22) =22990a(23) =37975a(24) =62721a(25) =103598a(26) =171121a(27) =282646a(28) =466852a(29) =771119