a(n) = Sum_{k=0..floor(2*n/7)} binomial(2*n-4*k,3*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =5a(5) =21a(6) =57a(7) =122a(8) =249a(9) =575a(10) =1485a(11) =3830a(12) =9369a(13) =22107a(14) =52226a(15) =125925a(16) =307653a(17) =750275a(18) =1815191a(19) =4371772a(20) =10539893a(21) =25488736a(22) =61735922a(23) =149450118a(24) =361364501a(25) =873306464a(26) =2111040783a(27) =5105279903a(28) =12348599802a(29) =29865304188