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

Terms

a(0) =1a(1) =1a(2) =1a(3) =5a(4) =9a(5) =17a(6) =41a(7) =85a(8) =177a(9) =385a(10) =817a(11) =1733a(12) =3705a(13) =7889a(14) =16793a(15) =35797a(16) =76257a(17) =162433a(18) =346081a(19) =737285a(20) =1570665a(21) =3346193a(22) =7128713a(23) =15186901a(24) =32354193a(25) =68927233a(26) =146842129a(27) =312831941a(28) =666455769a(29) =1419814097