a(n) = 3*a(n-1) - 4*a(n-3) + a(n-6).

Terms

a(0) =4a(1) =9a(2) =20a(3) =44a(4) =96a(5) =209a(6) =455a(7) =990a(8) =2154a(9) =4686a(10) =10194a(11) =22175a(12) =48236a(13) =104922a(14) =228220a(15) =496402a(16) =1079712a(17) =2348431a(18) =5107921a(19) =11109837a(20) =24164007a(21) =52556739a(22) =114310581a(23) =248624146a(24) =540753403a(25) =1176127722a(26) =2558050589a(27) =5563694894