a(n) = Sum_{k=0..floor(2*n/7)} binomial(2*n-5*k,2*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =4a(5) =11a(6) =22a(7) =38a(8) =71a(9) =149a(10) =316a(11) =639a(12) =1257a(13) =2493a(14) =5031a(15) =10196a(16) =20538a(17) =41168a(18) =82561a(19) =165995a(20) =334074a(21) =671856a(22) =1350078a(23) =2712818a(24) =5453022a(25) =10963211a(26) =22039707a(27) =44301549a(28) =89047335a(29) =178996043