a(n) = (3*b(n) + b(n-1) + 1)/2, where b = A005409.

Terms

a(0) =2a(1) =7a(2) =19a(3) =48a(4) =118a(5) =287a(6) =695a(7) =1680a(8) =4058a(9) =9799a(10) =23659a(11) =57120a(12) =137902a(13) =332927a(14) =803759a(15) =1940448a(16) =4684658a(17) =11309767a(18) =27304195a(19) =65918160a(20) =159140518a(21) =384199199a(22) =927538919a(23) =2239277040a(24) =5406093002a(25) =13051463047a(26) =31509019099a(27) =76069501248a(28) =183648021598a(29) =443365544447