a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =1a(7) =1a(8) =2a(9) =5a(10) =11a(11) =21a(12) =36a(13) =57a(14) =85a(15) =121a(16) =167a(17) =228a(18) =315a(19) =449a(20) =666a(21) =1023a(22) =1605a(23) =2533a(24) =3974a(25) =6156a(26) =9394a(27) =14137a(28) =21051a(29) =31159