a(n) = 2*a(n-1) + a(n-3), where a(0) = 0, a(1) = 1, a(2) = 4.

Terms

a(0) =0a(1) =1a(2) =4a(3) =8a(4) =17a(5) =38a(6) =84a(7) =185a(8) =408a(9) =900a(10) =1985a(11) =4378a(12) =9656a(13) =21297a(14) =46972a(15) =103600a(16) =228497a(17) =503966a(18) =1111532a(19) =2451561a(20) =5407088a(21) =11925708a(22) =26302977a(23) =58013042a(24) =127951792a(25) =282206561a(26) =622426164a(27) =1372804120a(28) =3027814801a(29) =6678055766