a(n) = (1/2) * (5*P(n+1) + P(n) - 1), where P(k) are the Pell numbers A000129.

Terms

a(0) =2a(1) =5a(2) =13a(3) =32a(4) =78a(5) =189a(6) =457a(7) =1104a(8) =2666a(9) =6437a(10) =15541a(11) =37520a(12) =90582a(13) =218685a(14) =527953a(15) =1274592a(16) =3077138a(17) =7428869a(18) =17934877a(19) =43298624a(20) =104532126a(21) =252362877a(22) =609257881a(23) =1470878640a(24) =3551015162a(25) =8572908965a(26) =20696833093a(27) =49966575152a(28) =120629983398a(29) =291226541949