a(n) = 3a(n-1)+a(n-2)+a(n-3), a(0)=1, a(1)=1, a(2)=5.

Terms

a(0) =1a(1) =1a(2) =5a(3) =17a(4) =57a(5) =193a(6) =653a(7) =2209a(8) =7473a(9) =25281a(10) =85525a(11) =289329a(12) =978793a(13) =3311233a(14) =11201821a(15) =37895489a(16) =128199521a(17) =433695873a(18) =1467182629a(19) =4963443281a(20) =16791208345a(21) =56804250945a(22) =192167404461a(23) =650097672673