a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0,0,1,1.

Terms

a(0) =0a(1) =0a(2) =1a(3) =1a(4) =4a(5) =12a(6) =33a(7) =97a(8) =280a(9) =808a(10) =2337a(11) =6753a(12) =19516a(13) =56404a(14) =163009a(15) =471105a(16) =1361520a(17) =3934864a(18) =11371969a(19) =32865601a(20) =94983348a(21) =274506972a(22) =793339873a(23) =2292794785a(24) =6626299912a(25) =19150362168a(26) =55345573857a(27) =159951677089a(28) =462268926316