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

Terms

a(0) =0a(1) =1a(2) =2a(3) =6a(4) =13a(5) =32a(6) =72a(7) =169a(8) =386a(9) =894a(10) =2053a(11) =4736a(12) =10896a(13) =25105a(14) =57794a(15) =133110a(16) =306493a(17) =705824a(18) =1625304a(19) =3742777a(20) =8618690a(21) =19847022a(22) =45703093a(23) =105244160a(24) =242353440a(25) =558085921a(26) =1285146242a(27) =2959404006a(28) =6814842733a(29) =15693054752