a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) for n > 2, a(0)=1, a(1)=4, a(2)=10.

Terms

a(0) =1a(1) =4a(2) =10a(3) =24a(4) =54a(5) =118a(6) =252a(7) =530a(8) =1102a(9) =2272a(10) =4654a(11) =9486a(12) =19260a(13) =38986a(14) =78726a(15) =158672a(16) =319318a(17) =641830a(18) =1288828a(19) =2586018a(20) =5185566a(21) =10393024a(22) =20821470a(23) =41700254a(24) =83493244a(25) =167136538a(26) =334515862a(27) =669424560a(28) =1339484742a(29) =2679997942