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

Terms

a(0) =1a(1) =2a(2) =6a(3) =15a(4) =37a(5) =90a(6) =218a(7) =527a(8) =1273a(9) =3074a(10) =7422a(11) =17919a(12) =43261a(13) =104442a(14) =252146a(15) =608735a(16) =1469617a(17) =3547970a(18) =8565558a(19) =20679087a(20) =49923733a(21) =120526554a(22) =290976842a(23) =702480239a(24) =1695937321a(25) =4094354882a(26) =9884647086a(27) =23863649055a(28) =57611945197