a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 8.

Terms

a(0) =1a(1) =8a(2) =8a(3) =17a(4) =33a(5) =58a(6) =108a(7) =199a(8) =365a(9) =672a(10) =1236a(11) =2273a(12) =4181a(13) =7690a(14) =14144a(15) =26015a(16) =47849a(17) =88008a(18) =161872a(19) =297729a(20) =547609a(21) =1007210a(22) =1852548a(23) =3407367a(24) =6267125a(25) =11527040a(26) =21201532a(27) =38995697a(28) =71724269a(29) =131921498