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

Terms

a(0) =1a(1) =1a(2) =6a(3) =7a(4) =23a(5) =30a(6) =73a(7) =103a(8) =211a(9) =314a(10) =581a(11) =895a(12) =1560a(13) =2455a(14) =4135a(15) =6590a(16) =10890a(17) =17480a(18) =28590a(19) =46070a(20) =74946a(21) =121016a(22) =196326a(23) =317342a(24) =514123a(25) =831465a(26) =1346148a(27) =2177613a(28) =3524441a(29) =5702054