a(n) = Sum_{k=0..floor(2*n/9)} binomial(2*n-7*k,2*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =4a(6) =11a(7) =22a(8) =37a(9) =57a(10) =94a(11) =176a(12) =347a(13) =667a(14) =1219a(15) =2158a(16) =3823a(17) =6913a(18) =12728a(19) =23513a(20) =43106a(21) =78338a(22) =141889a(23) =257571a(24) =469463a(25) =857602a(26) =1566006a(27) =2854694a(28) =5197179a(29) =9460622