a(n)=n for n<=3; thereafter a(n)=a(n-1)+a(n-2)+a(n-3)+1.

Terms

a(0) =0a(1) =1a(2) =2a(3) =3a(4) =7a(5) =13a(6) =24a(7) =45a(8) =83a(9) =153a(10) =282a(11) =519a(12) =955a(13) =1757a(14) =3232a(15) =5945a(16) =10935a(17) =20113a(18) =36994a(19) =68043a(20) =125151a(21) =230189a(22) =423384a(23) =778725a(24) =1432299a(25) =2634409a(26) =4845434a(27) =8912143a(28) =16391987a(29) =30149565